Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
260 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 85 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. #22551591 | C4 | semidirect |
| 10. #22551591 | C4 | semidirect |
| 11. #22551583 | C4 | semidirect |
| 12. #22551583 | C4 | semidirect |
| 33. #16861602 | Q8 | semidirect |
| 55. M16×C257 | Q8 | semidirect |
| 114. C257 | #1986 | semidirect |
| 152. M16 | Dic514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657290 | 2 |
| M16×Dic257 | 2 |
| C4×#16861597 | 2 |
| #30656498 | 2 |
| #30656497 | 2 |
| #30656496 | 2 |
| #339×C257 | 2 |
| #1986 | 257 |