| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 18T738 |
$C_3^6:(D_4\times A_4)$ |
$69984$ |
$-1$ |
✓ |
$-1$ |
$76$ |
$C_2$, $C_3$, $C_6$ |
18T738, 24T16098 x 2, 27T1236, 36T17608 x 2, 36T17609 x 2, 36T17610 x 2, 36T17611 x 2, 36T17612 x 2, 36T17613 x 2, 36T17614 x 4, 36T17615 x 4, 36T17616 x 4, 36T17617 x 4, 36T17618 x 2, 36T17780 x 2, 36T17806 x 2, 36T17939 |
| 18T739 |
$C_3^6.(C_2^2\times S_4)$ |
$69984$ |
$-1$ |
✓ |
$-1$ |
$115$ |
$C_2$, $S_3$, $D_{6}$ |
24T16108, 27T1246, 36T17619, 36T17620, 36T17621, 36T17622, 36T17623, 36T17624, 36T17625, 36T17788, 36T17791 x 2, 36T17794, 36T17796, 36T17923 |
| 18T740 |
$C_3\wr A_4:C_2^3$ |
$69984$ |
$-1$ |
✓ |
$-1$ |
$174$ |
$S_3$, $S_4\times C_2$ |
18T740 x 2, 27T1244 x 3, 36T17626 x 3, 36T17627 x 3, 36T17628 x 3, 36T17629 x 3, 36T17630 x 3, 36T17631 x 3, 36T17632 x 3, 36T17789 x 3, 36T17792 x 3 |
| 18T741 |
$C_3^6:(C_4\times S_4)$ |
$69984$ |
$1$ |
✓ |
$-1$ |
$70$ |
$C_2$, $S_3$, $D_{6}$ |
18T741, 24T16110 x 2, 27T1234, 36T17633 x 2, 36T17634 x 2, 36T17635 x 2, 36T17636 x 2, 36T17637 x 2, 36T17638 x 2, 36T17639 x 2, 36T17798 x 2, 36T17802 x 2, 36T17940 |
| 18T742 |
$C_3^3.C_6^3:A_4$ |
$69984$ |
$-1$ |
✓ |
$-1$ |
$159$ |
$C_3$, $A_4\times C_2$ |
18T742 x 2, 27T1251 x 3, 36T17640 x 3, 36T17641 x 3, 36T17642 x 6, 36T17643 x 6, 36T17644 x 6, 36T17645 x 6, 36T17646 x 6, 36T17647 x 6, 36T17648 x 3, 36T17832 x 3, 36T17833 x 3 |
| 18T743 |
$C_3^3.S_3^3:A_4$ |
$69984$ |
$1$ |
✓ |
$-1$ |
$138$ |
$C_3$, $A_4$ |
18T743 x 2, 27T1252 x 3, 36T17649 x 3, 36T17650 x 3, 36T17651 x 3, 36T17652 x 3, 36T17653 x 3, 36T17654 x 3, 36T17655 x 12, 36T17656 x 12, 36T17657 x 3, 36T17821 x 6 |
| 18T744 |
$C_3^6:(C_4^2:C_6)$ |
$69984$ |
$-1$ |
✓ |
$-1$ |
$56$ |
$C_3$, $A_4$ |
18T747, 27T1240, 36T17658, 36T17659, 36T17660, 36T17661, 36T17662, 36T17663, 36T17664, 36T17681, 36T17682, 36T17683 x 2, 36T17684 x 2, 36T17685 |
| 18T745 |
$C_3^6:(C_2^3:A_4)$ |
$69984$ |
$-1$ |
✓ |
$-1$ |
$69$ |
$C_2$, $C_3$, $C_6$ |
18T748, 24T16094, 24T16095 x 2, 27T1254, 36T17665, 36T17666, 36T17667 x 2, 36T17668 x 2, 36T17669 x 2, 36T17670 x 2, 36T17671 x 2, 36T17672 x 2, 36T17673, 36T17686, 36T17687, 36T17688, 36T17689, 36T17690, 36T17691, 36T17692, 36T17834, 36T17835 |
| 18T746 |
$(C_3:S_3)^3.A_4$ |
$69984$ |
$1$ |
✓ |
$-1$ |
$56$ |
$C_3$, $A_4$ |
18T746, 27T1245, 36T17674 x 2, 36T17675 x 2, 36T17676 x 2, 36T17677 x 2, 36T17678 x 2, 36T17679 x 2, 36T17680 x 2 |
| 18T747 |
$C_3^6:(C_4^2:C_6)$ |
$69984$ |
$-1$ |
✓ |
$-1$ |
$56$ |
$C_3$, $A_4\times C_2$ |
18T744, 27T1240, 36T17658, 36T17659, 36T17660, 36T17661, 36T17662, 36T17663, 36T17664, 36T17681, 36T17682, 36T17683 x 2, 36T17684 x 2, 36T17685 |
| 18T748 |
$C_3^6:(C_2^3:A_4)$ |
$69984$ |
$-1$ |
✓ |
$-1$ |
$69$ |
$C_3$, $A_4$ |
18T745, 24T16094, 24T16095 x 2, 27T1254, 36T17665, 36T17666, 36T17667 x 2, 36T17668 x 2, 36T17669 x 2, 36T17670 x 2, 36T17671 x 2, 36T17672 x 2, 36T17673, 36T17686, 36T17687, 36T17688, 36T17689, 36T17690, 36T17691, 36T17692, 36T17834, 36T17835 |
| 18T749 |
$C_3^6.\GL(2,\mathbb{Z}/4)$ |
$69984$ |
$-1$ |
✓ |
$-1$ |
$73$ |
$C_2$, $S_3$, $S_3$ |
18T751, 18T752 x 2, 24T16099, 24T16109, 27T1231 x 2, 27T1243, 36T17693, 36T17694, 36T17695, 36T17696, 36T17697, 36T17698, 36T17699 x 2, 36T17700 x 2, 36T17701 x 2, 36T17702 x 2, 36T17703, 36T17711, 36T17712, 36T17713, 36T17714, 36T17715, 36T17716, 36T17717, 36T17718 x 2, 36T17719 x 2, 36T17720 x 2, 36T17721 x 2, 36T17722 x 2, 36T17723 x 2, 36T17724 x 2, 36T17781, 36T17797, 36T17801, 36T17944 |
| 18T750 |
$C_3^5:D_6:D_{12}$ |
$69984$ |
$-1$ |
✓ |
$-1$ |
$64$ |
$C_2$, $S_3$, $D_{6}$ |
18T750, 24T16111 x 2, 27T1242, 36T17704 x 2, 36T17705 x 2, 36T17706 x 2, 36T17707 x 2, 36T17708 x 2, 36T17709 x 2, 36T17710 x 2, 36T17799 x 2, 36T17800 x 2, 36T17943 |
| 18T751 |
$C_3^6.\GL(2,\mathbb{Z}/4)$ |
$69984$ |
$-1$ |
✓ |
$-1$ |
$73$ |
$C_2$, $S_3$, $D_{6}$ |
18T749, 18T752 x 2, 24T16099, 24T16109, 27T1231 x 2, 27T1243, 36T17693, 36T17694, 36T17695, 36T17696, 36T17697, 36T17698, 36T17699 x 2, 36T17700 x 2, 36T17701 x 2, 36T17702 x 2, 36T17703, 36T17711, 36T17712, 36T17713, 36T17714, 36T17715, 36T17716, 36T17717, 36T17718 x 2, 36T17719 x 2, 36T17720 x 2, 36T17721 x 2, 36T17722 x 2, 36T17723 x 2, 36T17724 x 2, 36T17781, 36T17797, 36T17801, 36T17944 |
| 18T752 |
$C_3^6.\GL(2,\mathbb{Z}/4)$ |
$69984$ |
$-1$ |
✓ |
$-1$ |
$73$ |
$S_3$, $S_4\times C_2$ |
18T749, 18T751, 18T752, 24T16099, 24T16109, 27T1231 x 2, 27T1243, 36T17693, 36T17694, 36T17695, 36T17696, 36T17697, 36T17698, 36T17699 x 2, 36T17700 x 2, 36T17701 x 2, 36T17702 x 2, 36T17703, 36T17711, 36T17712, 36T17713, 36T17714, 36T17715, 36T17716, 36T17717, 36T17718 x 2, 36T17719 x 2, 36T17720 x 2, 36T17721 x 2, 36T17722 x 2, 36T17723 x 2, 36T17724 x 2, 36T17781, 36T17797, 36T17801, 36T17944 |
| 18T753 |
$(C_3:S_3)^3.A_4$ |
$69984$ |
$1$ |
✓ |
$-1$ |
$58$ |
$C_3$, $A_4$ |
18T753, 27T1249, 36T17725 x 2, 36T17726 x 2, 36T17727 x 4, 36T17728 x 4, 36T17729 x 2, 36T17820 x 2 |
| 18T754 |
$C_3^6.C_2^4.S_3$ |
$69984$ |
$1$ |
✓ |
$-1$ |
$87$ |
$S_3$, $S_4$ |
27T1239, 36T17730, 36T17731, 36T17732 x 2, 36T17733 x 2, 36T17734, 36T17837 x 2, 36T17840 |
| 18T755 |
$C_3^5:D_6:S_4$ |
$69984$ |
$1$ |
✓ |
$-1$ |
$123$ |
$S_3$, $S_4$ |
27T1228, 36T17735, 36T17736, 36T17737 x 2, 36T17738 x 2, 36T17739, 36T17836 x 2, 36T17841 |
| 18T756 |
$C_3^5:D_6.S_4$ |
$69984$ |
$1$ |
✓ |
$-1$ |
$65$ |
$S_3$, $S_4$ |
18T756, 27T1230, 36T17740 x 2, 36T17741 x 2, 36T17742 x 4, 36T17743 x 4, 36T17744 x 2 |
| 18T757 |
$C_3^5:D_6:S_4$ |
$69984$ |
$-1$ |
✓ |
$-1$ |
$72$ |
$S_3$, $S_4$ |
18T757 x 2, 18T761, 24T16096, 24T16097 x 2, 27T1229 x 3, 36T17745 x 3, 36T17746 x 3, 36T17747 x 3, 36T17748 x 3, 36T17749 x 3, 36T17750 x 3, 36T17751 x 3, 36T17767 x 2, 36T17768 x 3, 36T17769 x 3, 36T17770 x 6, 36T17771, 36T17843 |
| 18T758 |
$C_3^5:D_6.S_4$ |
$69984$ |
$-1$ |
✓ |
$-1$ |
$53$ |
$S_3$, $S_4$ |
18T762, 27T1241, 36T17752, 36T17753, 36T17754, 36T17755, 36T17756, 36T17757, 36T17758, 36T17772, 36T17773, 36T17774 |
| 18T759 |
$C_3^6.C_2^2:S_4$ |
$69984$ |
$-1$ |
✓ |
$-1$ |
$102$ |
$S_3$, $S_4$ |
27T1248, 36T17759, 36T17760, 36T17761, 36T17838, 36T17839, 36T17842 |
| 18T760 |
$C_3^5:D_6.S_4$ |
$69984$ |
$1$ |
✓ |
$-1$ |
$41$ |
$S_3$, $S_4$ |
18T760, 27T1233, 36T17762 x 2, 36T17763 x 2, 36T17764 x 4, 36T17765 x 4, 36T17766 x 2 |
| 18T761 |
$C_3^5:D_6:S_4$ |
$69984$ |
$-1$ |
✓ |
$-1$ |
$72$ |
$C_2$, $S_3$, $S_3$ |
18T757 x 3, 24T16096, 24T16097 x 2, 27T1229 x 3, 36T17745 x 3, 36T17746 x 3, 36T17747 x 3, 36T17748 x 3, 36T17749 x 3, 36T17750 x 3, 36T17751 x 3, 36T17767 x 2, 36T17768 x 3, 36T17769 x 3, 36T17770 x 6, 36T17771, 36T17843 |
| 18T762 |
$C_3^5:D_6.S_4$ |
$69984$ |
$-1$ |
✓ |
$-1$ |
$53$ |
$S_3$, $S_4$ |
18T758, 27T1241, 36T17752, 36T17753, 36T17754, 36T17755, 36T17756, 36T17757, 36T17758, 36T17772, 36T17773, 36T17774 |
| 18T763 |
$C_2^8.F_9:C_2^2$ |
$73728$ |
$-1$ |
✓ |
$-1$ |
$78$ |
$(C_3^2:C_8):C_2$ |
18T763 x 3, 24T16230 x 2, 24T16231 x 2, 32T1831856 x 2, 32T1831858 x 2, 36T18278, 36T18280 x 2, 36T18312 x 2, 36T18360, 36T18362 x 2, 36T18364 x 2, 36T18366 x 2, 36T18373 x 4, 36T18374 x 4, 36T18375 x 4, 36T18376 x 4, 36T18766 x 2, 36T18767 x 2 |
| 18T764 |
$C_2\times A_4^3.S_4$ |
$82944$ |
$-1$ |
✓ |
$-1$ |
$192$ |
$S_3$, $C_3 \wr S_3 $ |
18T764, 24T16570 x 2, 36T19023, 36T19026, 36T19032 x 2, 36T19033 x 2, 36T19099, 36T19100 x 2, 36T19108 x 2, 36T19152 x 2, 36T19153 x 2, 36T19154 x 2, 36T19155 x 2, 36T19383 x 2, 36T19385 x 2, 36T19389 x 4, 36T19390 x 4 |
| 18T765 |
$S_4^3.C_6$ |
$82944$ |
$-1$ |
✓ |
$-1$ |
$110$ |
$C_3$, $S_3 \wr C_3 $ |
18T765, 18T767 x 4, 18T768 x 2, 24T16590 x 2, 24T16591 x 2, 24T16592 x 4, 36T19079 x 4, 36T19080 x 4, 36T19081 x 4, 36T19082 x 4, 36T19096, 36T19097, 36T19098 x 2, 36T19101 x 2, 36T19102 x 2, 36T19105 x 2, 36T19106 x 2, 36T19143 x 4, 36T19144 x 4, 36T19145 x 4, 36T19146 x 4, 36T19147 x 4, 36T19148 x 4, 36T19149 x 4, 36T19150 x 4, 36T19157 x 2, 36T19158 x 2, 36T19159 x 2, 36T19160 x 2, 36T19161 x 4, 36T19162 x 4, 36T19164 x 2, 36T19165 x 2, 36T19166 x 2, 36T19167 x 2, 36T19168 x 4, 36T19169 x 4, 36T19412 x 2, 36T19413 x 2 |
| 18T766 |
$A_4^3.(C_2^2\times A_4)$ |
$82944$ |
$-1$ |
✓ |
$-1$ |
$144$ |
$C_3$, $(C_3^3:C_3):C_2$ |
18T766 x 5, 24T16568 x 6, 36T19022 x 3, 36T19043 x 6, 36T19044 x 6, 36T19085 x 6, 36T19086 x 6, 36T19109 x 6, 36T19110 x 6, 36T19136 x 6, 36T19137 x 6, 36T19138 x 6, 36T19139 x 6, 36T19140 x 12, 36T19141 x 12, 36T19384 x 3 |
| 18T767 |
$S_4^3.C_6$ |
$82944$ |
$-1$ |
✓ |
$-1$ |
$110$ |
$C_3$, $S_3 \wr C_3 $ |
18T765 x 2, 18T767 x 3, 18T768 x 2, 24T16590 x 2, 24T16591 x 2, 24T16592 x 4, 36T19079 x 4, 36T19080 x 4, 36T19081 x 4, 36T19082 x 4, 36T19096, 36T19097, 36T19098 x 2, 36T19101 x 2, 36T19102 x 2, 36T19105 x 2, 36T19106 x 2, 36T19143 x 4, 36T19144 x 4, 36T19145 x 4, 36T19146 x 4, 36T19147 x 4, 36T19148 x 4, 36T19149 x 4, 36T19150 x 4, 36T19157 x 2, 36T19158 x 2, 36T19159 x 2, 36T19160 x 2, 36T19161 x 4, 36T19162 x 4, 36T19164 x 2, 36T19165 x 2, 36T19166 x 2, 36T19167 x 2, 36T19168 x 4, 36T19169 x 4, 36T19412 x 2, 36T19413 x 2 |
| 18T768 |
$S_4^3.C_6$ |
$82944$ |
$-1$ |
✓ |
$-1$ |
$110$ |
$C_3$, $S_3 \wr C_3 $ |
18T765 x 2, 18T767 x 4, 18T768, 24T16590 x 2, 24T16591 x 2, 24T16592 x 4, 36T19079 x 4, 36T19080 x 4, 36T19081 x 4, 36T19082 x 4, 36T19096, 36T19097, 36T19098 x 2, 36T19101 x 2, 36T19102 x 2, 36T19105 x 2, 36T19106 x 2, 36T19143 x 4, 36T19144 x 4, 36T19145 x 4, 36T19146 x 4, 36T19147 x 4, 36T19148 x 4, 36T19149 x 4, 36T19150 x 4, 36T19157 x 2, 36T19158 x 2, 36T19159 x 2, 36T19160 x 2, 36T19161 x 4, 36T19162 x 4, 36T19164 x 2, 36T19165 x 2, 36T19166 x 2, 36T19167 x 2, 36T19168 x 4, 36T19169 x 4, 36T19412 x 2, 36T19413 x 2 |
| 18T769 |
$C_2\times A_4^3:S_4$ |
$82944$ |
$-1$ |
✓ |
$-1$ |
$80$ |
$S_3$, $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ |
18T769, 18T782 x 2, 24T16586 x 2, 24T16587 x 2, 36T19118 x 2, 36T19126, 36T19127, 36T19128, 36T19129, 36T19130 x 2, 36T19197 x 2, 36T19198 x 2, 36T19199 x 2, 36T19200 x 2, 36T19259 x 2, 36T19260 x 2, 36T19261 x 2, 36T19262 x 2, 36T19417 x 2, 36T19419 x 2 |
| 18T770 |
$A_4^3.(C_2\times S_4)$ |
$82944$ |
$-1$ |
✓ |
$-1$ |
$65$ |
$S_3$, $S_3\wr S_3$ |
12T294, 18T773, 18T776, 18T777, 18T779, 18T780, 18T783, 18T785, 24T16593, 24T16594, 24T16595, 24T16596, 24T16597, 24T16598, 24T16599, 36T19182, 36T19183, 36T19184, 36T19185, 36T19192, 36T19193, 36T19194, 36T19195, 36T19211, 36T19212, 36T19213, 36T19214, 36T19215, 36T19216, 36T19219, 36T19220, 36T19221, 36T19222, 36T19229, 36T19230, 36T19231, 36T19232, 36T19247, 36T19248, 36T19249, 36T19250, 36T19251, 36T19252, 36T19254, 36T19255, 36T19256, 36T19257, 36T19420, 36T19421, 36T19422, 36T19423 |
| 18T771 |
$A_4^3.(C_2\times S_4)$ |
$82944$ |
$1$ |
✓ |
$-1$ |
$84$ |
$S_3$, $((C_3^3:C_3):C_2):C_2$ |
18T774, 18T775, 18T778, 24T16581, 24T16582, 24T16583, 24T16584, 36T19050, 36T19051, 36T19052, 36T19053, 36T19058, 36T19059, 36T19061, 36T19062, 36T19177, 36T19178, 36T19179, 36T19180, 36T19207, 36T19208, 36T19209, 36T19210, 36T19235, 36T19236, 36T19237, 36T19238, 36T19239, 36T19240, 36T19242, 36T19243, 36T19244, 36T19245, 36T19398, 36T19399 |
| 18T772 |
$C_2\times A_4^3.S_4$ |
$82944$ |
$-1$ |
✓ |
$-1$ |
$144$ |
$S_3$, $(C_3^3:C_3):C_2$ |
18T772, 24T16572 x 2, 36T19028, 36T19030, 36T19055 x 2, 36T19056 x 2, 36T19131, 36T19132 x 2, 36T19134 x 2, 36T19202 x 2, 36T19203 x 2, 36T19204 x 2, 36T19205 x 2, 36T19388, 36T19418 x 2 |
| 18T773 |
$A_4^3.(C_2\times S_4)$ |
$82944$ |
$-1$ |
✓ |
$-1$ |
$65$ |
$S_3$, $S_3\wr S_3$ |
12T294, 18T770, 18T776, 18T777, 18T779, 18T780, 18T783, 18T785, 24T16593, 24T16594, 24T16595, 24T16596, 24T16597, 24T16598, 24T16599, 36T19182, 36T19183, 36T19184, 36T19185, 36T19192, 36T19193, 36T19194, 36T19195, 36T19211, 36T19212, 36T19213, 36T19214, 36T19215, 36T19216, 36T19219, 36T19220, 36T19221, 36T19222, 36T19229, 36T19230, 36T19231, 36T19232, 36T19247, 36T19248, 36T19249, 36T19250, 36T19251, 36T19252, 36T19254, 36T19255, 36T19256, 36T19257, 36T19420, 36T19421, 36T19422, 36T19423 |
| 18T774 |
$A_4^3.(C_2\times S_4)$ |
$82944$ |
$-1$ |
✓ |
$-1$ |
$84$ |
$S_3$, $((C_3^3:C_3):C_2):C_2$ |
18T771, 18T775, 18T778, 24T16581, 24T16582, 24T16583, 24T16584, 36T19050, 36T19051, 36T19052, 36T19053, 36T19058, 36T19059, 36T19061, 36T19062, 36T19177, 36T19178, 36T19179, 36T19180, 36T19207, 36T19208, 36T19209, 36T19210, 36T19235, 36T19236, 36T19237, 36T19238, 36T19239, 36T19240, 36T19242, 36T19243, 36T19244, 36T19245, 36T19398, 36T19399 |
| 18T775 |
$A_4^3.(C_2\times S_4)$ |
$82944$ |
$-1$ |
✓ |
$-1$ |
$84$ |
$S_3$, $((C_3^3:C_3):C_2):C_2$ |
18T771, 18T774, 18T778, 24T16581, 24T16582, 24T16583, 24T16584, 36T19050, 36T19051, 36T19052, 36T19053, 36T19058, 36T19059, 36T19061, 36T19062, 36T19177, 36T19178, 36T19179, 36T19180, 36T19207, 36T19208, 36T19209, 36T19210, 36T19235, 36T19236, 36T19237, 36T19238, 36T19239, 36T19240, 36T19242, 36T19243, 36T19244, 36T19245, 36T19398, 36T19399 |
| 18T776 |
$A_4^3.(C_2\times S_4)$ |
$82944$ |
$1$ |
✓ |
$-1$ |
$65$ |
$S_3$, $S_3\wr S_3$ |
12T294, 18T770, 18T773, 18T777, 18T779, 18T780, 18T783, 18T785, 24T16593, 24T16594, 24T16595, 24T16596, 24T16597, 24T16598, 24T16599, 36T19182, 36T19183, 36T19184, 36T19185, 36T19192, 36T19193, 36T19194, 36T19195, 36T19211, 36T19212, 36T19213, 36T19214, 36T19215, 36T19216, 36T19219, 36T19220, 36T19221, 36T19222, 36T19229, 36T19230, 36T19231, 36T19232, 36T19247, 36T19248, 36T19249, 36T19250, 36T19251, 36T19252, 36T19254, 36T19255, 36T19256, 36T19257, 36T19420, 36T19421, 36T19422, 36T19423 |
| 18T777 |
$A_4^3.(C_2\times S_4)$ |
$82944$ |
$1$ |
✓ |
$-1$ |
$65$ |
$S_3$, $S_3\wr S_3$ |
12T294, 18T770, 18T773, 18T776, 18T779, 18T780, 18T783, 18T785, 24T16593, 24T16594, 24T16595, 24T16596, 24T16597, 24T16598, 24T16599, 36T19182, 36T19183, 36T19184, 36T19185, 36T19192, 36T19193, 36T19194, 36T19195, 36T19211, 36T19212, 36T19213, 36T19214, 36T19215, 36T19216, 36T19219, 36T19220, 36T19221, 36T19222, 36T19229, 36T19230, 36T19231, 36T19232, 36T19247, 36T19248, 36T19249, 36T19250, 36T19251, 36T19252, 36T19254, 36T19255, 36T19256, 36T19257, 36T19420, 36T19421, 36T19422, 36T19423 |
| 18T778 |
$A_4^3.(C_2\times S_4)$ |
$82944$ |
$-1$ |
✓ |
$-1$ |
$84$ |
$S_3$, $((C_3^3:C_3):C_2):C_2$ |
18T771, 18T774, 18T775, 24T16581, 24T16582, 24T16583, 24T16584, 36T19050, 36T19051, 36T19052, 36T19053, 36T19058, 36T19059, 36T19061, 36T19062, 36T19177, 36T19178, 36T19179, 36T19180, 36T19207, 36T19208, 36T19209, 36T19210, 36T19235, 36T19236, 36T19237, 36T19238, 36T19239, 36T19240, 36T19242, 36T19243, 36T19244, 36T19245, 36T19398, 36T19399 |
| 18T779 |
$A_4^3.(C_2\times S_4)$ |
$82944$ |
$-1$ |
✓ |
$-1$ |
$65$ |
$S_3$, $S_3\wr S_3$ |
12T294, 18T770, 18T773, 18T776, 18T777, 18T780, 18T783, 18T785, 24T16593, 24T16594, 24T16595, 24T16596, 24T16597, 24T16598, 24T16599, 36T19182, 36T19183, 36T19184, 36T19185, 36T19192, 36T19193, 36T19194, 36T19195, 36T19211, 36T19212, 36T19213, 36T19214, 36T19215, 36T19216, 36T19219, 36T19220, 36T19221, 36T19222, 36T19229, 36T19230, 36T19231, 36T19232, 36T19247, 36T19248, 36T19249, 36T19250, 36T19251, 36T19252, 36T19254, 36T19255, 36T19256, 36T19257, 36T19420, 36T19421, 36T19422, 36T19423 |
| 18T780 |
$A_4^3.(C_2\times S_4)$ |
$82944$ |
$-1$ |
✓ |
$-1$ |
$65$ |
$S_3$, $S_3\wr S_3$ |
12T294, 18T770, 18T773, 18T776, 18T777, 18T779, 18T783, 18T785, 24T16593, 24T16594, 24T16595, 24T16596, 24T16597, 24T16598, 24T16599, 36T19182, 36T19183, 36T19184, 36T19185, 36T19192, 36T19193, 36T19194, 36T19195, 36T19211, 36T19212, 36T19213, 36T19214, 36T19215, 36T19216, 36T19219, 36T19220, 36T19221, 36T19222, 36T19229, 36T19230, 36T19231, 36T19232, 36T19247, 36T19248, 36T19249, 36T19250, 36T19251, 36T19252, 36T19254, 36T19255, 36T19256, 36T19257, 36T19420, 36T19421, 36T19422, 36T19423 |
| 18T781 |
$C_2\times A_4^3:S_4$ |
$82944$ |
$-1$ |
✓ |
$-1$ |
$74$ |
$S_3$, $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ |
18T781, 18T784 x 2, 24T16588 x 2, 24T16589 x 2, 36T19114, 36T19115, 36T19116, 36T19120 x 2, 36T19121, 36T19122 x 2, 36T19187 x 2, 36T19188 x 2, 36T19189 x 2, 36T19190 x 2, 36T19224 x 2, 36T19225 x 2, 36T19226 x 2, 36T19227 x 2, 36T19415 x 2 |
| 18T782 |
$C_2\times A_4^3:S_4$ |
$82944$ |
$-1$ |
✓ |
$-1$ |
$80$ |
$S_3$, $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ |
18T769 x 2, 18T782, 24T16586 x 2, 24T16587 x 2, 36T19118 x 2, 36T19126, 36T19127, 36T19128, 36T19129, 36T19130 x 2, 36T19197 x 2, 36T19198 x 2, 36T19199 x 2, 36T19200 x 2, 36T19259 x 2, 36T19260 x 2, 36T19261 x 2, 36T19262 x 2, 36T19417 x 2, 36T19419 x 2 |
| 18T783 |
$A_4^3.(C_2\times S_4)$ |
$82944$ |
$-1$ |
✓ |
$-1$ |
$65$ |
$S_3$, $S_3\wr S_3$ |
12T294, 18T770, 18T773, 18T776, 18T777, 18T779, 18T780, 18T785, 24T16593, 24T16594, 24T16595, 24T16596, 24T16597, 24T16598, 24T16599, 36T19182, 36T19183, 36T19184, 36T19185, 36T19192, 36T19193, 36T19194, 36T19195, 36T19211, 36T19212, 36T19213, 36T19214, 36T19215, 36T19216, 36T19219, 36T19220, 36T19221, 36T19222, 36T19229, 36T19230, 36T19231, 36T19232, 36T19247, 36T19248, 36T19249, 36T19250, 36T19251, 36T19252, 36T19254, 36T19255, 36T19256, 36T19257, 36T19420, 36T19421, 36T19422, 36T19423 |
| 18T784 |
$C_2\times A_4^3:S_4$ |
$82944$ |
$-1$ |
✓ |
$-1$ |
$74$ |
$S_3$, $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ |
18T781 x 2, 18T784, 24T16588 x 2, 24T16589 x 2, 36T19114, 36T19115, 36T19116, 36T19120 x 2, 36T19121, 36T19122 x 2, 36T19187 x 2, 36T19188 x 2, 36T19189 x 2, 36T19190 x 2, 36T19224 x 2, 36T19225 x 2, 36T19226 x 2, 36T19227 x 2, 36T19415 x 2 |
| 18T785 |
$A_4^3.(C_2\times S_4)$ |
$82944$ |
$-1$ |
✓ |
$-1$ |
$65$ |
$S_3$, $S_3\wr S_3$ |
12T294, 18T770, 18T773, 18T776, 18T777, 18T779, 18T780, 18T783, 24T16593, 24T16594, 24T16595, 24T16596, 24T16597, 24T16598, 24T16599, 36T19182, 36T19183, 36T19184, 36T19185, 36T19192, 36T19193, 36T19194, 36T19195, 36T19211, 36T19212, 36T19213, 36T19214, 36T19215, 36T19216, 36T19219, 36T19220, 36T19221, 36T19222, 36T19229, 36T19230, 36T19231, 36T19232, 36T19247, 36T19248, 36T19249, 36T19250, 36T19251, 36T19252, 36T19254, 36T19255, 36T19256, 36T19257, 36T19420, 36T19421, 36T19422, 36T19423 |
| 18T786 |
$A_4:S_4^2.A_4$ |
$82944$ |
$1$ |
✓ |
$-1$ |
$96$ |
$C_3$, $((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ |
18T786 x 11, 24T16585 x 12, 36T19066 x 12, 36T19068 x 6, 36T19264 x 12, 36T19265 x 12, 36T19266 x 12, 36T19267 x 12, 36T19268 x 24, 36T19269 x 24, 36T19401 x 6 |
| 18T787 |
$C_3\wr S_5$ |
$87480$ |
$-1$ |
|
$-1$ |
$120$ |
$\PGL(2,5)$ |
18T787 x 2, 36T19445 x 3, 45T973 x 3 |
Results are complete for degrees $\leq 23$.
