Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
176 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. #30657084 | C2 | semidirect |
| 2. #30657027 | C2 | semidirect |
| 4. #30656488 | C2 | semidirect |
| 5. #30656485 | C2 | semidirect |
| 6. #30656480 | C2 | semidirect |
| 7. C8×D4×C257 | C2 | semidirect |
| 82. C257 | #1677 | semidirect |
| 87. C8×D4 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657084 | 2 |
| #30657027 | 2 |
| #30656932 | 2 |
| #30656488 | 2 |
| #30656485 | 2 |
| #30656480 | 2 |
| C8×D4×C257 | 2 |
| #1677 | 257 |