Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
256 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 61 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. C2×#22551536 | C2 | semidirect |
| 2. #30656978 | C2 | semidirect |
| 3. #30656538 | C2 | semidirect |
| 4. C22⋊#16861593 | C2 | semidirect |
| 6. C2×Dic1028 | C22 | semidirect |
| 9. C2×#16861593 | C22 | semidirect |
| 10. #22551526 | C22 | semidirect |
| 59. C22×C257 | SD32 | semidirect |
| 71. C257 | #2187 | semidirect |
| 131. C22 | #22551536 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551536 | 2 |
| #30656978 | 2 |
| #30656538 | 2 |
| C22⋊#16861593 | 2 |
| C22×D8×C257 | 2 |
| #2187 | 257 |