Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
230 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 19. #106×C257 | C4 | semidirect |
| 96. C257 | #1920 | semidirect |
| 114. #106 | Dic257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30656636 | 2 |
| C4⋊C4×Dic257 | 2 |
| #30656500 | 2 |
| #30656499 | 2 |
| #30656491 | 2 |
| C2×#106×C257 | 2 |
| #1920 | 257 |