| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 12T130 |
$C_3\wr C_2^2$ |
$324$ |
$1$ |
✓ |
$-1$ |
$45$ |
$C_2$ x 3, $C_2^2$ |
12T130, 18T120 x 6, 36T494 x 6, 36T517, 36T523 x 3, 36T530 x 6, 36T535 x 6, 36T541 x 2 |
| 18T120 |
$C_3\wr C_2^2$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$45$ |
$C_2$, $S_3\times C_3$, $S_3^2$ |
12T130 x 2, 18T120 x 5, 36T494 x 6, 36T517, 36T523 x 3, 36T530 x 6, 36T535 x 6, 36T541 x 2 |
| 36T494 |
$C_3\wr C_2^2$ |
$324$ |
$1$ |
✓ |
$-1$ |
$45$ |
$C_2$ x 3, $C_2^2$, $S_3\times C_3$, $S_3^2$, $S_3^2$, $C_6\times S_3$, $C_3\wr C_2^2$, $C_3\wr C_2^2$ |
12T130 x 2, 18T120 x 6, 36T494 x 5, 36T517, 36T523 x 3, 36T530 x 6, 36T535 x 6, 36T541 x 2 |
| 36T517 |
$C_3\wr C_2^2$ |
$324$ |
$1$ |
✓ |
$-1$ |
$45$ |
$C_2$ x 3, $C_3$, $C_2^2$, $C_6$ x 3, $C_6\times C_2$, $C_3:S_3^2$, $C_3\wr C_2^2$ x 2 |
12T130 x 2, 18T120 x 6, 36T494 x 6, 36T523 x 3, 36T530 x 6, 36T535 x 6, 36T541 x 2 |
| 36T523 |
$C_3\wr C_2^2$ |
$324$ |
$1$ |
✓ |
$-1$ |
$45$ |
$C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2, $D_6$, $C_3\times S_3^2$, $C_3\wr C_2^2$ x 2 |
12T130 x 2, 18T120 x 6, 36T494 x 6, 36T517, 36T523 x 2, 36T530 x 6, 36T535 x 6, 36T541 x 2 |
| 36T530 |
$C_3\wr C_2^2$ |
$324$ |
$1$ |
✓ |
$-1$ |
$45$ |
$C_2$ x 3, $C_2^2$, $S_3^2$, $S_3^2$, $C_3\times S_3^2$ x 2, $C_3\wr C_2^2$ |
12T130 x 2, 18T120 x 6, 36T494 x 6, 36T517, 36T523 x 3, 36T530 x 5, 36T535 x 6, 36T541 x 2 |
| 36T535 |
$C_3\wr C_2^2$ |
$324$ |
$1$ |
✓ |
$-1$ |
$45$ |
$C_2$ x 3, $C_2^2$, $S_3\times C_3$, $C_6\times S_3$, $C_3\times S_3^2$, $C_3:S_3^2$, $C_3\wr C_2^2$ |
12T130 x 2, 18T120 x 6, 36T494 x 6, 36T517, 36T523 x 3, 36T530 x 6, 36T535 x 5, 36T541 x 2 |
| 36T541 |
$C_3\wr C_2^2$ |
$324$ |
$1$ |
✓ |
$-1$ |
$45$ |
$C_2$ x 3, $C_2^2$, $C_3\times S_3^2$ x 3, $C_3:S_3^2$ |
12T130 x 2, 18T120 x 6, 36T494 x 6, 36T517, 36T523 x 3, 36T530 x 6, 36T535 x 6, 36T541 |
Results are complete for degrees $\leq 23$.
