Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
272 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 133 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 |
|---|---|---|
| 10. #22551524 | C4 | semidirect |
| 11. #22551502 | C4 | semidirect |
| 15. #107×C257 | C4 | semidirect |
| 50. C8×C257 | C42 | semidirect |
| 68. C257 | #1776 | semidirect |
| 81. #107 | Dic257 | semidirect |
| 119. C8 | C4×Dic257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22551524 | 2 |
| C2×#22551502 | 2 |
| C4⋊C4×Dic257 | 2 |
| #30656499 | 2 |
| C2×#107×C257 | 2 |
| #1776 | 257 |