| Label |
Name |
Order |
Parity |
Solvable |
Nil. class |
Conj. classes |
Subfields |
Low Degree Siblings |
| 18T301 |
$C_2\times C_3^3:S_4$ |
$1296$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$S_3$, $S_4\times C_2$, $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ |
18T301, 18T313 x 2, 24T2878 x 4, 24T2880 x 2, 36T2134, 36T2135, 36T2136, 36T2137 x 2, 36T2138 x 2, 36T2144 x 2, 36T2145, 36T2146 x 2 |
| 18T313 |
$C_2\times C_3^3:S_4$ |
$1296$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $S_3$, $D_{6}$, $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$ |
18T301 x 2, 18T313, 24T2878 x 4, 24T2880 x 2, 36T2134, 36T2135, 36T2136, 36T2137 x 2, 36T2138 x 2, 36T2144 x 2, 36T2145, 36T2146 x 2 |
| 24T2878 |
$C_2\times C_3^3:S_4$ |
$1296$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $S_4$, $S_4\times C_2$, $C_3^3:S_4$ |
18T301 x 2, 18T313 x 2, 24T2878 x 3, 24T2880 x 2, 36T2134, 36T2135, 36T2136, 36T2137 x 2, 36T2138 x 2, 36T2144 x 2, 36T2145, 36T2146 x 2 |
| 24T2880 |
$C_2\times C_3^3:S_4$ |
$1296$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $S_4$, $S_4\times C_2$, $C_3^3:S_4$ |
18T301 x 2, 18T313 x 2, 24T2878 x 4, 24T2880, 36T2134, 36T2135, 36T2136, 36T2137 x 2, 36T2138 x 2, 36T2144 x 2, 36T2145, 36T2146 x 2 |
| 36T2134 |
$C_2\times C_3^3:S_4$ |
$1296$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $S_3$, $S_3$, $S_4\times C_2$ x 2, $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$, $C_2\times S_4$, $C_3^3:S_4$ |
18T301 x 2, 18T313 x 2, 24T2878 x 4, 24T2880 x 2, 36T2135, 36T2136, 36T2137 x 2, 36T2138 x 2, 36T2144 x 2, 36T2145, 36T2146 x 2 |
| 36T2135 |
$C_2\times C_3^3:S_4$ |
$1296$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_2$ x 3, $S_3$, $C_2^2$, $S_3$, $D_{6}$ x 2, $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$, $D_6$, $C_3^3:S_4$, $C_2\times C_3^3:S_4$ x 2 |
18T301 x 2, 18T313 x 2, 24T2878 x 4, 24T2880 x 2, 36T2134, 36T2136, 36T2137 x 2, 36T2138 x 2, 36T2144 x 2, 36T2145, 36T2146 x 2 |
| 36T2136 |
$C_2\times C_3^3:S_4$ |
$1296$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $S_3$, $S_3$, $S_4\times C_2$ x 2, $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$, $C_2\times S_4$, $C_3^3:S_4$, $C_2\times C_3^3:S_4$ x 2 |
18T301 x 2, 18T313 x 2, 24T2878 x 4, 24T2880 x 2, 36T2134, 36T2135, 36T2137 x 2, 36T2138 x 2, 36T2144 x 2, 36T2145, 36T2146 x 2 |
| 36T2137 |
$C_2\times C_3^3:S_4$ |
$1296$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $S_3$, $D_{6}$, $S_4$, $S_4\times C_2$, $C_2 \times S_4$, $C_3^3:S_4$ |
18T301 x 2, 18T313 x 2, 24T2878 x 4, 24T2880 x 2, 36T2134, 36T2135, 36T2136, 36T2137, 36T2138 x 2, 36T2144 x 2, 36T2145, 36T2146 x 2 |
| 36T2138 |
$C_2\times C_3^3:S_4$ |
$1296$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$S_3$, $S_4$, $C_2 \times S_4$, $C_3^3:S_4$ |
18T301 x 2, 18T313 x 2, 24T2878 x 4, 24T2880 x 2, 36T2134, 36T2135, 36T2136, 36T2137 x 2, 36T2138, 36T2144 x 2, 36T2145, 36T2146 x 2 |
| 36T2144 |
$C_2\times C_3^3:S_4$ |
$1296$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $S_3$, $D_{6}$, $S_4$, $S_4\times C_2$, $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$, $C_2 \times S_4$, $C_3^3:S_4$, $C_2\times C_3^3:S_4$, $C_2\times C_3^3:S_4$ |
18T301 x 2, 18T313 x 2, 24T2878 x 4, 24T2880 x 2, 36T2134, 36T2135, 36T2136, 36T2137 x 2, 36T2138 x 2, 36T2144, 36T2145, 36T2146 x 2 |
| 36T2145 |
$C_2\times C_3^3:S_4$ |
$1296$ |
$-1$ |
✓ |
$-1$ |
$28$ |
$S_3$, $S_4$, $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$, $C_2 \times S_4$, $C_3^3:S_4$ |
18T301 x 2, 18T313 x 2, 24T2878 x 4, 24T2880 x 2, 36T2134, 36T2135, 36T2136, 36T2137 x 2, 36T2138 x 2, 36T2144 x 2, 36T2146 x 2 |
| 36T2146 |
$C_2\times C_3^3:S_4$ |
$1296$ |
$1$ |
✓ |
$-1$ |
$28$ |
$C_2$, $S_3$, $D_{6}$, $S_4$, $S_4\times C_2$, $(((C_3 \times (C_3^2 : C_2)) : C_2) : C_3) : C_2$, $C_2 \times S_4$, $C_3^3:S_4$, $C_2\times C_3^3:S_4$, $C_2\times C_3^3:S_4$ |
18T301 x 2, 18T313 x 2, 24T2878 x 4, 24T2880 x 2, 36T2134, 36T2135, 36T2136, 36T2137 x 2, 36T2138 x 2, 36T2144 x 2, 36T2145, 36T2146 |
Results are complete for degrees $\leq 23$.
