Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
216 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 71 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. #30656785 | C2 | semidirect |
| 4. C4×#16861602 | C2 | semidirect |
| 5. #30656508 | C2 | semidirect |
| 6. #30656497 | C2 | semidirect |
| 14. #22551511 | C4 | semidirect |
| 15. #22551509 | C4 | semidirect |
| 95. C257 | #1932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30656785 | 2 |
| #30656754 | 2 |
| #30656721 | 2 |
| C4×#16861602 | 2 |
| #30656508 | 2 |
| #30656497 | 2 |
| C2×#104×C257 | 2 |
| #1932 | 257 |