Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
232 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 9. #22551526 | C4 | semidirect |
| 10. #22551524 | C4 | semidirect |
| 13. C8×Dic257 | C4 | semidirect |
| 16. #108×C257 | C4 | semidirect |
| 64. C257 | #1772 | semidirect |
| 76. #108 | Dic257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30656775 | 2 |
| #30656695 | 2 |
| C2×C8×Dic257 | 2 |
| #30656498 | 2 |
| C2×#108×C257 | 2 |
| #1772 | 257 |