| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 18T66 |
$C_6:S_4$ |
$144$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$S_3$ x 4, $S_4\times C_2$, $C_3^2:C_2$ |
18T66, 24T251 x 6, 36T109, 36T133 x 2, 36T134 x 2, 36T166 |
| 24T251 |
$C_6:S_4$ |
$144$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $S_3$, $S_4$, $D_{6}$, $S_4\times C_2$, $C_3:S_4$ |
18T66 x 2, 24T251 x 5, 36T109, 36T133 x 2, 36T134 x 2, 36T166 |
| 36T109 |
$C_6:S_4$ |
$144$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $S_3$ x 4, $S_3$ x 4, $S_4\times C_2$ x 2, $C_3^2:C_2$, $C_2\times S_4$, $C_3^2 : C_2$, $C_6:S_4$ x 2 |
18T66 x 2, 24T251 x 6, 36T133 x 2, 36T134 x 2, 36T166 |
| 36T133 |
$C_6:S_4$ |
$144$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $S_3$ x 4, $D_{6}$ x 4, $S_4$, $S_4\times C_2$, $C_3^2:C_2$, $C_2 \times S_4$, $C_6:S_3$, $C_3:S_4$, $C_6:S_4$ |
18T66 x 2, 24T251 x 6, 36T109, 36T133, 36T134 x 2, 36T166 |
| 36T134 |
$C_6:S_4$ |
$144$ |
$1$ |
✓ |
$-1$ |
$18$ |
$C_2$, $S_3$ x 4, $D_{6}$ x 4, $S_4$, $S_4\times C_2$, $C_3^2:C_2$, $C_2 \times S_4$, $C_6:S_3$, $C_3:S_4$, $C_6:S_4$ |
18T66 x 2, 24T251 x 6, 36T109, 36T133 x 2, 36T134, 36T166 |
| 36T166 |
$C_6:S_4$ |
$144$ |
$-1$ |
✓ |
$-1$ |
$18$ |
$S_3$ x 4, $S_4$, $C_3^2:C_2$, $C_2 \times S_4$, $C_3:S_4$ |
18T66 x 2, 24T251 x 6, 36T109, 36T133 x 2, 36T134 x 2 |
Results are complete for degrees $\leq 23$.
