| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 12T131 |
$C_3\wr C_4$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $C_4$ |
12T131 x 3, 18T123 x 4, 36T497 x 4, 36T514 x 2, 36T527 x 2, 36T532 x 4, 36T536 x 4, 36T543 x 4, 36T544 x 8 |
| 18T123 |
$C_3\wr C_4$ |
$324$ |
$1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $S_3\times C_3$, $C_3^2:C_4$ |
12T131 x 4, 18T123 x 3, 36T497 x 4, 36T514 x 2, 36T527 x 2, 36T532 x 4, 36T536 x 4, 36T543 x 4, 36T544 x 8 |
| 36T497 |
$C_3\wr C_4$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $C_4$, $S_3\times C_3$, $C_3^2:C_4$, $(C_3\times C_3):C_4$, $C_3\times (C_3 : C_4)$, $C_3\wr C_4$, $C_3\wr C_4$ |
12T131 x 4, 18T123 x 4, 36T497 x 3, 36T514 x 2, 36T527 x 2, 36T532 x 4, 36T536 x 4, 36T543 x 4, 36T544 x 8 |
| 36T514 |
$C_3\wr C_4$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $C_3$, $C_4$, $C_6$, $C_{12}$, $C_3^3:C_4$, $C_3\wr C_4$ x 2 |
12T131 x 4, 18T123 x 4, 36T497 x 4, 36T514, 36T527 x 2, 36T532 x 4, 36T536 x 4, 36T543 x 4, 36T544 x 8 |
| 36T527 |
$C_3\wr C_4$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $S_3$, $C_4$, $S_3$, $C_3 : C_4$, $C_3^2:C_{12}$, $C_3\wr C_4$ x 2 |
12T131 x 4, 18T123 x 4, 36T497 x 4, 36T514 x 2, 36T527, 36T532 x 4, 36T536 x 4, 36T543 x 4, 36T544 x 8 |
| 36T532 |
$C_3\wr C_4$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $C_4$, $C_3^2:C_4$, $(C_3\times C_3):C_4$, $C_3\wr C_4$ x 3 |
12T131 x 4, 18T123 x 4, 36T497 x 4, 36T514 x 2, 36T527 x 2, 36T532 x 3, 36T536 x 4, 36T543 x 4, 36T544 x 8 |
| 36T536 |
$C_3\wr C_4$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $C_4$, $S_3\times C_3$, $C_3\times (C_3 : C_4)$, $C_3^3:C_4$, $C_3^2:C_{12}$, $C_3\wr C_4$ |
12T131 x 4, 18T123 x 4, 36T497 x 4, 36T514 x 2, 36T527 x 2, 36T532 x 4, 36T536 x 3, 36T543 x 4, 36T544 x 8 |
| 36T543 |
$C_3\wr C_4$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $C_4$, $C_3^3:C_4$, $C_3^2:C_{12}$, $C_3\wr C_4$ |
12T131 x 4, 18T123 x 4, 36T497 x 4, 36T514 x 2, 36T527 x 2, 36T532 x 4, 36T536 x 4, 36T543 x 3, 36T544 x 8 |
| 36T544 |
$C_3\wr C_4$ |
$324$ |
$-1$ |
✓ |
$-1$ |
$36$ |
$C_2$, $C_4$, $C_3^3:C_4$, $C_3^2:C_{12}$, $C_3\wr C_4$ x 2 |
12T131 x 4, 18T123 x 4, 36T497 x 4, 36T514 x 2, 36T527 x 2, 36T532 x 4, 36T536 x 4, 36T543 x 4, 36T544 x 7 |
Results are complete for degrees $\leq 23$.
