Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 240 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 |
|---|---|---|
| 4. #30656484 | C2 | semidirect |
| 5. #30656483 | C2 | semidirect |
| 6. #30656482 | C2 | semidirect |
| 7. #332×C257 | C2 | semidirect |
| 91. C257 | #1549 | semidirect |
| 99. #332 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D257 | 2 |
| #30656789 | 2 |
| #30656759 | 2 |
| #30656484 | 2 |
| #30656483 | 2 |
| #30656482 | 2 |
| #332×C257 | 2 |
| #1549 | 257 |