Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
2550 conjugacy classes of subgroups.
The subgroup lattice has 348 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C131 | C24 |
| commutator | C22 | C24×C4×C131 |
| Frattini, cosocle | C23 | C25×C131 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C24×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #2356×C131 | C2 | direct (N × H) |
| 11. C2×C4×Q8×C131 | C4 | semidirect |
| 47. C4×Q8×C131 | C2×C4 | semidirect |
| 167. C2×C131 | #2356 | direct (N × H) |
| 173. C2×#2356 | C131 | direct (N × H) |
| 174. C131 | C2×#2356 | direct (N × H) |
| 176. #2356 | C2×C131 | direct (N × H) |
| 185. C2×C4×Q8 | C4×C131 | semidirect |
| 221. C4×Q8 | C2×C4×C131 | semidirect |
| 341. C2 | #2356×C131 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Q8×C131 | 2 |
| #2356×C131 | 2 |
| C2×#391×C131 | 2 |
| C2×#387×C131 | 2 |
| C2×#383×C131 | 2 |
| C2×#382×C131 | 2 |
| C2×C4×C4⋊C4×C131 | 2 |
| C2×#376×C131 | 2 |
| C2×#2356 | 131 |