Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
464 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 213 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. #30656644 | C2 | semidirect |
| 2. #30656636 | C2 | semidirect |
| 5. #30656623 | C2 | semidirect |
| 6. #30656623 | C2 | semidirect |
| 28. C22⋊Q8×C257 | C4 | semidirect |
| 110. C257 | #2378 | semidirect |
| 123. C22⋊Q8 | Dic257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30656644 | 2 |
| #30656636 | 2 |
| #30656630 | 2 |
| #30656623 | 2 |
| #30656600 | 2 |
| #30656597 | 2 |
| C2×C22⋊Q8×C257 | 2 |
| #2378 | 257 |