Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 3. #30656746 | C2 | semidirect |
| 5. #30656498 | C2 | semidirect |
| 6. #30656496 | C2 | semidirect |
| 7. #419×C257 | C2 | semidirect |
| 11. #22551581 | C4 | semidirect |
| 42. C4×Dic257 | C2×C4 | semidirect |
| 48. C2×Q8×C257 | C2×C4 | semidirect |
| 107. C257 | #1885 | semidirect |
| 112. #419 | D257 | semidirect |
| 138. C2×Q8 | C4×D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551581 | 2 |
| #30657211 | 2 |
| #30656746 | 2 |
| C2×#22551508 | 2 |
| #30656498 | 2 |
| #30656496 | 2 |
| #419×C257 | 2 |
| #1885 | 257 |