| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 12T169 |
$C_3^3:D_{12}$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $D_{4}$ |
12T169, 18T210 x 2, 24T1521 x 2, 24T1533, 36T1105 x 2, 36T1106 x 2, 36T1107 x 2, 36T1153, 36T1154, 36T1160, 36T1167, 36T1173, 36T1190 x 2, 36T1195 x 2, 36T1225 x 2 |
| 18T210 |
$C_3^3:D_{12}$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3^2$, $C_3^2:D_4$ |
12T169 x 2, 18T210, 24T1521 x 2, 24T1533, 36T1105 x 2, 36T1106 x 2, 36T1107 x 2, 36T1153, 36T1154, 36T1160, 36T1167, 36T1173, 36T1190 x 2, 36T1195 x 2, 36T1225 x 2 |
| 24T1521 |
$C_3^3:D_{12}$ |
$648$ |
$1$ |
✓ |
$-1$ |
$30$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$, $C_3^3:D_{12}$ |
12T169 x 2, 18T210 x 2, 24T1521, 24T1533, 36T1105 x 2, 36T1106 x 2, 36T1107 x 2, 36T1153, 36T1154, 36T1160, 36T1167, 36T1173, 36T1190 x 2, 36T1195 x 2, 36T1225 x 2 |
| 24T1533 |
$C_3^3:D_{12}$ |
$648$ |
$1$ |
✓ |
$-1$ |
$30$ |
$C_2$ x 3, $C_2^2$, $D_{4}$ x 2, $D_4$ |
12T169 x 2, 18T210 x 2, 24T1521 x 2, 36T1105 x 2, 36T1106 x 2, 36T1107 x 2, 36T1153, 36T1154, 36T1160, 36T1167, 36T1173, 36T1190 x 2, 36T1195 x 2, 36T1225 x 2 |
| 36T1105 |
$C_3^3:D_{12}$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $D_{4}$, $S_3^2$, $C_3^2:D_4$, $\SOPlus(4,2)$, $C_3:D_{12}$, $C_3^3:D_{12}$, $C_3^3:D_{12}$ |
12T169 x 2, 18T210 x 2, 24T1521 x 2, 24T1533, 36T1105, 36T1106 x 2, 36T1107 x 2, 36T1153, 36T1154, 36T1160, 36T1167, 36T1173, 36T1190 x 2, 36T1195 x 2, 36T1225 x 2 |
| 36T1106 |
$C_3^3:D_{12}$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $D_{4}$, $S_3^2$, $C_3^2:D_4$, $\SOPlus(4,2)$, $C_3:D_{12}$, $C_3^3:D_{12}$ |
12T169 x 2, 18T210 x 2, 24T1521 x 2, 24T1533, 36T1105 x 2, 36T1106, 36T1107 x 2, 36T1153, 36T1154, 36T1160, 36T1167, 36T1173, 36T1190 x 2, 36T1195 x 2, 36T1225 x 2 |
| 36T1107 |
$C_3^3:D_{12}$ |
$648$ |
$1$ |
✓ |
$-1$ |
$30$ |
$C_2$ x 3, $C_2^2$, $S_3^2$, $C_3^2:D_4$, $S_3^2$, $\SOPlus(4,2)$, $C_3^3:D_{12}$ |
12T169 x 2, 18T210 x 2, 24T1521 x 2, 24T1533, 36T1105 x 2, 36T1106 x 2, 36T1107, 36T1153, 36T1154, 36T1160, 36T1167, 36T1173, 36T1190 x 2, 36T1195 x 2, 36T1225 x 2 |
| 36T1153 |
$C_3^3:D_{12}$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3$, $D_{4}$, $D_{6}$, $D_{12}$, $S_3^2:S_3$ |
12T169 x 2, 18T210 x 2, 24T1521 x 2, 24T1533, 36T1105 x 2, 36T1106 x 2, 36T1107 x 2, 36T1154, 36T1160, 36T1167, 36T1173, 36T1190 x 2, 36T1195 x 2, 36T1225 x 2 |
| 36T1154 |
$C_3^3:D_{12}$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3$, $D_{4}$, $D_{6}$, $D_{12}$, $S_3^2:S_3$, $C_3^3:D_{12}$ x 2 |
12T169 x 2, 18T210 x 2, 24T1521 x 2, 24T1533, 36T1105 x 2, 36T1106 x 2, 36T1107 x 2, 36T1153, 36T1160, 36T1167, 36T1173, 36T1190 x 2, 36T1195 x 2, 36T1225 x 2 |
| 36T1160 |
$C_3^3:D_{12}$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3$, $D_{4}$, $D_{6}$, $(C_6\times C_2):C_2$, $C_3^2:D_{12}$, $C_3^3:D_{12}$ x 2 |
12T169 x 2, 18T210 x 2, 24T1521 x 2, 24T1533, 36T1105 x 2, 36T1106 x 2, 36T1107 x 2, 36T1153, 36T1154, 36T1167, 36T1173, 36T1190 x 2, 36T1195 x 2, 36T1225 x 2 |
| 36T1167 |
$C_3^3:D_{12}$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $S_3$, $D_{4}$, $S_3$, $(C_6\times C_2):C_2$, $C_3^2:D_{12}$ |
12T169 x 2, 18T210 x 2, 24T1521 x 2, 24T1533, 36T1105 x 2, 36T1106 x 2, 36T1107 x 2, 36T1153, 36T1154, 36T1160, 36T1173, 36T1190 x 2, 36T1195 x 2, 36T1225 x 2 |
| 36T1173 |
$C_3^3:D_{12}$ |
$648$ |
$1$ |
✓ |
$-1$ |
$30$ |
$C_2$ x 3, $C_2^2$, $S_3^2$, $C_3^2:D_4$, $S_3^2$, $\SOPlus(4,2)$ |
12T169 x 2, 18T210 x 2, 24T1521 x 2, 24T1533, 36T1105 x 2, 36T1106 x 2, 36T1107 x 2, 36T1153, 36T1154, 36T1160, 36T1167, 36T1190 x 2, 36T1195 x 2, 36T1225 x 2 |
| 36T1190 |
$C_3^3:D_{12}$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $D_{4}$, $C_3^2:D_4$, $\SOPlus(4,2)$, $C_3^3:D_{12}$ |
12T169 x 2, 18T210 x 2, 24T1521 x 2, 24T1533, 36T1105 x 2, 36T1106 x 2, 36T1107 x 2, 36T1153, 36T1154, 36T1160, 36T1167, 36T1173, 36T1190, 36T1195 x 2, 36T1225 x 2 |
| 36T1195 |
$C_3^3:D_{12}$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $D_{4}$, $S_3^2$, $C_3:D_{12}$, $C_3^2:D_{12}$, $S_3^2:S_3$, $C_3^3:D_{12}$ |
12T169 x 2, 18T210 x 2, 24T1521 x 2, 24T1533, 36T1105 x 2, 36T1106 x 2, 36T1107 x 2, 36T1153, 36T1154, 36T1160, 36T1167, 36T1173, 36T1190 x 2, 36T1195, 36T1225 x 2 |
| 36T1225 |
$C_3^3:D_{12}$ |
$648$ |
$-1$ |
✓ |
$-1$ |
$30$ |
$C_2$, $D_{4}$, $S_3^2:S_3$, $C_3^2:D_{12}$ |
12T169 x 2, 18T210 x 2, 24T1521 x 2, 24T1533, 36T1105 x 2, 36T1106 x 2, 36T1107 x 2, 36T1153, 36T1154, 36T1160, 36T1167, 36T1173, 36T1190 x 2, 36T1195 x 2, 36T1225 |
Results are complete for degrees $\leq 23$.
