Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
136 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 7. #22551528 | C4 | semidirect |
| 13. C2×C16×C257 | C4 | semidirect |
| 55. C257 | #1383 | semidirect |
| 65. C2×C16 | Dic257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551528 | 2 |
| C2×#22551524 | 2 |
| C2×M32×C257 | 2 |
| #1383 | 257 |