Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
232 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 75 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. #30656777 | C2 | semidirect |
| 4. #30656692 | C2 | semidirect |
| 5. #30656506 | C2 | semidirect |
| 6. #30656502 | C2 | semidirect |
| 16. #22551509 | C4 | semidirect |
| 100. C257 | #1931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30656777 | 2 |
| #30656742 | 2 |
| C2×#22551509 | 2 |
| #30656692 | 2 |
| #30656506 | 2 |
| #30656502 | 2 |
| C2×#102×C257 | 2 |
| #1931 | 257 |