| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 18T152 |
$C_6^2:D_6$ |
$432$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$S_3$, $S_4$, $C_3^2 : D_{6} $ |
18T153, 18T154, 18T155, 36T608, 36T609, 36T611, 36T612, 36T623, 36T624, 36T627, 36T628, 36T687, 36T688, 36T701 |
| 18T153 |
$C_6^2:D_6$ |
$432$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$S_3$, $S_4\times C_2$, $C_3^2 : D_{6} $ |
18T152, 18T154, 18T155, 36T608, 36T609, 36T611, 36T612, 36T623, 36T624, 36T627, 36T628, 36T687, 36T688, 36T701 |
| 18T154 |
$C_6^2:D_6$ |
$432$ |
$1$ |
✓ |
$-1$ |
$20$ |
$S_3$, $S_4$, $C_3^2 : D_{6} $ |
18T152, 18T153, 18T155, 36T608, 36T609, 36T611, 36T612, 36T623, 36T624, 36T627, 36T628, 36T687, 36T688, 36T701 |
| 18T155 |
$C_6^2:D_6$ |
$432$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$S_3$, $S_4\times C_2$, $C_3^2 : D_{6} $ |
18T152, 18T153, 18T154, 36T608, 36T609, 36T611, 36T612, 36T623, 36T624, 36T627, 36T628, 36T687, 36T688, 36T701 |
| 36T608 |
$C_6^2:D_6$ |
$432$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3$, $S_3$, $S_4$, $S_4$, $C_3^2 : D_{6} $, $S_4$, $C_3^2:D_6$ |
18T152, 18T153, 18T154, 18T155, 36T609, 36T611, 36T612, 36T623, 36T624, 36T627, 36T628, 36T687, 36T688, 36T701 |
| 36T609 |
$C_6^2:D_6$ |
$432$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3$, $S_3$, $S_4\times C_2$ x 2, $C_3^2 : D_{6} $, $C_2\times S_4$, $C_3^2:D_6$ |
18T152, 18T153, 18T154, 18T155, 36T608, 36T611, 36T612, 36T623, 36T624, 36T627, 36T628, 36T687, 36T688, 36T701 |
| 36T611 |
$C_6^2:D_6$ |
$432$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3$, $S_3$, $S_4\times C_2$ x 2, $C_3^2 : D_{6} $, $C_2\times S_4$, $C_3^2:D_6$, $C_6^2:D_6$, $C_6^2:D_6$ |
18T152, 18T153, 18T154, 18T155, 36T608, 36T609, 36T612, 36T623, 36T624, 36T627, 36T628, 36T687, 36T688, 36T701 |
| 36T612 |
$C_6^2:D_6$ |
$432$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3$, $S_3$, $S_4$, $S_4$, $C_3^2 : D_{6} $, $S_4$, $C_3^2:D_6$, $C_6^2:D_6$, $C_6^2:D_6$ |
18T152, 18T153, 18T154, 18T155, 36T608, 36T609, 36T611, 36T623, 36T624, 36T627, 36T628, 36T687, 36T688, 36T701 |
| 36T623 |
$C_6^2:D_6$ |
$432$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3$, $D_{6}$, $S_4$, $S_4\times C_2$, $C_3^2 : D_{6} $, $C_2 \times S_4$, $C_3^2:D_6$, $C_6^2:D_6$, $C_6^2:D_6$ |
18T152, 18T153, 18T154, 18T155, 36T608, 36T609, 36T611, 36T612, 36T624, 36T627, 36T628, 36T687, 36T688, 36T701 |
| 36T624 |
$C_6^2:D_6$ |
$432$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3$, $D_{6}$, $S_4$, $S_4\times C_2$, $C_3^2 : D_{6} $, $C_2 \times S_4$, $C_3^2:D_6$, $C_6^2:D_6$, $C_6^2:D_6$ |
18T152, 18T153, 18T154, 18T155, 36T608, 36T609, 36T611, 36T612, 36T623, 36T627, 36T628, 36T687, 36T688, 36T701 |
| 36T627 |
$C_6^2:D_6$ |
$432$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3$, $D_{6}$, $S_4$, $S_4\times C_2$, $C_3^2 : D_{6} $, $C_2 \times S_4$, $C_3^2:D_6$, $C_6^2:D_6$, $C_6^2:D_6$ |
18T152, 18T153, 18T154, 18T155, 36T608, 36T609, 36T611, 36T612, 36T623, 36T624, 36T628, 36T687, 36T688, 36T701 |
| 36T628 |
$C_6^2:D_6$ |
$432$ |
$1$ |
✓ |
$-1$ |
$20$ |
$C_2$, $S_3$, $D_{6}$, $S_4$, $S_4\times C_2$, $C_3^2 : D_{6} $, $C_2 \times S_4$, $C_3^2:D_6$, $C_6^2:D_6$, $C_6^2:D_6$ |
18T152, 18T153, 18T154, 18T155, 36T608, 36T609, 36T611, 36T612, 36T623, 36T624, 36T627, 36T687, 36T688, 36T701 |
| 36T687 |
$C_6^2:D_6$ |
$432$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$S_3$, $S_4$, $S_4$, $C_3^2 : D_{6} $, $S_4$, $C_6^2:D_6$ |
18T152, 18T153, 18T154, 18T155, 36T608, 36T609, 36T611, 36T612, 36T623, 36T624, 36T627, 36T628, 36T688, 36T701 |
| 36T688 |
$C_6^2:D_6$ |
$432$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$S_3$, $S_4$, $C_3^2 : D_{6} $, $C_2 \times S_4$, $C_6^2:D_6$ |
18T152, 18T153, 18T154, 18T155, 36T608, 36T609, 36T611, 36T612, 36T623, 36T624, 36T627, 36T628, 36T687, 36T701 |
| 36T701 |
$C_6^2:D_6$ |
$432$ |
$-1$ |
✓ |
$-1$ |
$20$ |
$S_3$, $S_4$, $C_3^2 : D_{6} $, $S_3\times S_4$ |
18T152, 18T153, 18T154, 18T155, 36T608, 36T609, 36T611, 36T612, 36T623, 36T624, 36T627, 36T628, 36T687, 36T688 |
Results are complete for degrees $\leq 23$.
