Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
360 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 93 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. #30656745 | C2 | semidirect |
| 4. #30656496 | C2 | semidirect |
| 9. #22551579 | C4 | semidirect |
| 21. C2×Dic514 | C2×C4 | semidirect |
| 29. C4×Dic257 | C2×C4 | semidirect |
| 80. C257 | #1885 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551579 | 2 |
| #30656745 | 2 |
| C2×#22551509 | 2 |
| #30656496 | 2 |
| #518×C257 | 2 |
| #1885 | 257 |