Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
300 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×C8×Dic257 | C2 | semidirect |
| 5. #30656501 | C2 | semidirect |
| 6. #30656496 | C2 | semidirect |
| 7. #405×C257 | C2 | semidirect |
| 10. #22551598 | C4 | semidirect |
| 16. #22551518 | C4 | semidirect |
| 17. #22551515 | C4 | semidirect |
| 18. #22551512 | C4 | semidirect |
| 98. C257 | #1764 | semidirect |
| 103. #405 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551598 | 2 |
| C2×#22551518 | 2 |
| #30656731 | 2 |
| C2×C8×Dic257 | 2 |
| #30656501 | 2 |
| #30656496 | 2 |
| #405×C257 | 2 |
| #1764 | 257 |