Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
362 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 362 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×#22551523 | C2 | semidirect |
| 4. #30656633 | C2 | semidirect |
| 5. #30656500 | C2 | semidirect |
| 6. #30656491 | C2 | semidirect |
| 18. #22551513 | C4 | semidirect |
| 33. C2×#14523339 | C2×C4 | semidirect |
| 36. C4⋊Dic257 | C2×C4 | semidirect |
| 81. D4×C257 | C4⋊C4 | semidirect |
| 123. C257 | #1864 | semidirect |
| 191. D4 | #16861597 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic257 | 2 |
| C2×#22551523 | 2 |
| C2×#22551513 | 2 |
| #30656633 | 2 |
| #30656500 | 2 |
| #30656491 | 2 |
| C2×#102×C257 | 2 |
| #1864 | 257 |