Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
312 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 312 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 |
|---|---|---|
| 4. C2×#22551515 | C2 | semidirect |
| 5. C2×#22551510 | C2 | semidirect |
| 6. #30656501 | C2 | semidirect |
| 7. #343×C257 | C2 | semidirect |
| 11. #22551625 | C4 | semidirect |
| 116. C257 | #1908 | semidirect |
| 123. #343 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551625 | 2 |
| C2×#22551600 | 2 |
| #30656736 | 2 |
| C2×#22551515 | 2 |
| C2×#22551510 | 2 |
| #30656501 | 2 |
| #343×C257 | 2 |
| #1908 | 257 |