Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
464 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 173 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. #30656641 | C2 | semidirect |
| 3. #30656634 | C2 | semidirect |
| 6. #30656624 | C2 | semidirect |
| 7. #30656622 | C2 | semidirect |
| 11. #22551571 | C4 | semidirect |
| 110. C257 | #2378 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551571 | 2 |
| #30656641 | 2 |
| #30656634 | 2 |
| #30656631 | 2 |
| #30656625 | 2 |
| #30656624 | 2 |
| #30656622 | 2 |
| #30656597 | 2 |
| #381×C257 | 2 |
| #2378 | 257 |