Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
230 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 81 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. #30656764 | C2 | semidirect |
| 4. C2×C8×Dic257 | C2 | semidirect |
| 5. #30656502 | C2 | semidirect |
| 6. #30656496 | C2 | semidirect |
| 19. #103×C257 | C4 | semidirect |
| 20. #102×C257 | C4 | semidirect |
| 90. C257 | #1937 | semidirect |
| 108. #103 | Dic257 | semidirect |
| 109. #102 | Dic257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30656764 | 2 |
| C2×#22551519 | 2 |
| #30656704 | 2 |
| C2×C8×Dic257 | 2 |
| #30656502 | 2 |
| #30656496 | 2 |
| #416×C257 | 2 |
| #1937 | 257 |