Results (displaying all 34 matches)
| Label | Name | Order | Parity | Solvable | Subfields | Low Degree Siblings |
|---|---|---|---|---|---|---|
| 9T1 | $C_9$ | 9 | 1 | Yes | $C_3$ | |
| 9T2 | $C_3^2$ | 9 | 1 | Yes | $C_3$ x 4 | |
| 9T3 | $D_{9}$ | 18 | 1 | Yes | $S_3$ | 18T5 |
| 9T4 | $S_3\times C_3$ | 18 | -1 | Yes | $C_3$, $S_3$ | 6T5, 18T3 |
| 9T5 | $C_3^2:C_2$ | 18 | 1 | Yes | $S_3$ x 4 | 18T4 |
| 9T6 | $C_9:C_3$ | 27 | 1 | Yes | $C_3$ | 27T5 |
| 9T7 | $C_3^2:C_3$ | 27 | 1 | Yes | $C_3$ | 9T7 x 3, 27T3 |
| 9T8 | $S_3^2$ | 36 | -1 | Yes | $S_3$ x 2 | 6T9, 12T16, 18T9, 18T11 x 2, 36T13 |
| 9T9 | $C_3^2:C_4$ | 36 | 1 | Yes | 6T10 x 2, 12T17 x 2, 18T10, 36T14 | |
| 9T10 | $(C_9:C_3):C_2$ | 54 | 1 | Yes | $S_3$ | 18T18, 27T14 |
| 9T11 | $C_3^2 : C_6$ | 54 | 1 | Yes | $S_3$ | 9T13, 18T20, 18T21, 18T22, 27T11 |
| 9T12 | $(C_3^2:C_3):C_2$ | 54 | -1 | Yes | $S_3$ | 9T12 x 3, 18T24 x 4, 27T6 |
| 9T13 | $C_3^2 : S_3 $ | 54 | -1 | Yes | $C_3$ | 9T11, 18T20, 18T21, 18T22, 27T11 |
| 9T14 | $C_3^2:Q_8$ | 72 | 1 | Yes | 12T47, 18T35 x 3, 24T82, 36T55 | |
| 9T15 | $C_3^2:C_8$ | 72 | -1 | Yes | 12T46, 18T28, 24T81, 36T49 | |
| 9T16 | $S_3^2:C_2$ | 72 | -1 | Yes | 6T13 x 2, 12T34 x 2, 12T35 x 2, 12T36 x 2, 18T34 x 2, 18T36, 24T72 x 2, 36T53, 36T54 x 2 | |
| 9T17 | $C_3 \wr C_3 $ | 81 | 1 | Yes | $C_3$ | 9T17 x 2, 27T19, 27T21, 27T27 x 3 |
| 9T18 | $C_3^2 : D_{6} $ | 108 | -1 | Yes | $S_3$ | 9T18, 18T51 x 2, 18T55 x 2, 18T56, 18T57 x 2, 27T29, 36T87 x 2, 36T90 |
| 9T19 | $(C_3^2:C_8):C_2$ | 144 | -1 | Yes | 12T84, 18T68, 18T71, 18T73, 24T278, 24T279, 24T280, 36T171, 36T172, 36T175 | |
| 9T20 | $C_3 \wr S_3 $ | 162 | -1 | Yes | $S_3$ | 9T20 x 2, 18T86 x 3, 27T37, 27T50 x 3, 27T70 |
| 9T21 | $(C_3^3:C_3):C_2$ | 162 | 1 | Yes | $S_3$ | 9T21 x 2, 18T88 x 3, 27T51 x 3, 27T52, 27T67 |
| 9T22 | $(C_3^2:C_3):C_2$ | 162 | -1 | Yes | $C_3$ | 9T22 x 2, 18T85 x 3, 27T53 x 3, 27T62, 27T63 |
| 9T23 | $(C_3^2:Q_8):C_3$ | 216 | 1 | Yes | 12T122, 24T562, 24T569, 27T82, 36T287, 36T309 | |
| 9T24 | $((C_3^3:C_3):C_2):C_2$ | 324 | -1 | Yes | $S_3$ | 9T24 x 2, 18T129 x 3, 18T136 x 3, 18T137 x 3, 27T121, 27T128 x 3, 27T129, 36T502 x 3 |
| 9T25 | $((C_3 \times (C_3^2 : C_2)) : C_2) : C_3$ | 324 | 1 | Yes | $C_3$ | 12T132 x 2, 12T133, 18T141 x 2, 18T142, 18T143, 27T130, 27T131, 36T511, 36T512, 36T524, 36T546 x 2, 36T547 |
| 9T26 | $((C_3^2:Q_8):C_3):C_2$ | 432 | -1 | Yes | 12T157, 18T157, 24T1325, 24T1326, 24T1327, 24T1334, 27T139, 36T689, 36T709 | |
| 9T27 | $\PSL(2,8)$ | 504 | 1 | No | 28T70, 36T712 | |
| 9T28 | $S_3 \wr C_3 $ | 648 | -1 | Yes | $C_3$ | 12T176, 18T197 x 2, 18T198 x 2, 18T202, 18T204, 18T206, 18T207, 24T1528, 24T1539, 27T210, 27T213, 36T1094 x 2, 36T1095, 36T1096 x 2, 36T1097, 36T1099, 36T1101, 36T1102, 36T1103, 36T1137, 36T1238 |
| 9T29 | $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ | 648 | -1 | Yes | $S_3$ | 12T175, 18T219, 18T220, 18T223, 18T224, 24T1527, 24T1540, 27T214, 27T217, 36T1126, 36T1127, 36T1128, 36T1129, 36T1131, 36T1132, 36T1139, 36T1237 |
| 9T30 | $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ | 648 | 1 | Yes | $S_3$ | 12T177 x 2, 12T178, 18T217, 18T218, 18T221, 18T222, 24T1529 x 2, 24T1530, 27T211, 27T216, 36T1121, 36T1122, 36T1123, 36T1124, 36T1125, 36T1130, 36T1140, 36T1239 x 2, 36T1240 |
| 9T31 | $S_3\wr S_3$ | 1296 | -1 | Yes | $S_3$ | 12T213, 18T300, 18T303, 18T311, 18T312, 18T314, 18T315, 18T319, 18T320, 24T2893, 24T2894, 24T2895, 24T2912, 27T296, 27T298, 36T2197, 36T2198, 36T2199, 36T2201, 36T2202, 36T2210, 36T2211, 36T2212, 36T2213, 36T2214, 36T2215, 36T2216, 36T2217, 36T2218, 36T2219, 36T2220, 36T2225, 36T2226, 36T2229, 36T2305 |
| 9T32 | $\mathrm{P}\Gamma\mathrm{L}(2,8)$ | 1512 | 1 | No | 27T391, 28T165, 36T2342 | |
| 9T33 | $A_9$ | 181440 | 1 | No | 36T23796 | |
| 9T34 | $S_9$ | 362880 | -1 | No | 18T887, 36T28590 |
Results are complete for degrees $\leq 23$.