Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
360 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. C2×#22551526 | C2 | semidirect |
| 3. C2×#22551525 | C2 | semidirect |
| 6. #30656499 | C2 | semidirect |
| 7. #340×C257 | C2 | semidirect |
| 19. #22551504 | C4 | semidirect |
| 39. C2×#14523339 | C2×C4 | semidirect |
| 51. C2×C8×C257 | C2×C4 | semidirect |
| 105. C2×D257 | #107 | semidirect |
| 123. C257 | #1852 | semidirect |
| 131. #340 | D257 | semidirect |
| 169. C2×C8 | C4×D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×D257 | 2 |
| C2×#22551526 | 2 |
| C2×#22551525 | 2 |
| C2×#22551504 | 2 |
| #30656594 | 2 |
| #30656499 | 2 |
| #340×C257 | 2 |
| #1852 | 257 |