Finite Group DatabasebetaFinite Group DatabasebetaOrder 32896.
182 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 55 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. #30657085 | C2 | semidirect |
| 3. D4×#14523339 | C2 | semidirect |
| 4. #30656489 | C2 | semidirect |
| 5. #30656483 | C2 | semidirect |
| 6. #30656480 | C2 | semidirect |
| 7. #461×C257 | C2 | semidirect |
| 84. C257 | #1681 | semidirect |
| 87. #461 | D257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #30657085 | 2 |
| #30656932 | 2 |
| D4×#14523339 | 2 |
| #30656489 | 2 |
| #30656483 | 2 |
| #30656480 | 2 |
| #461×C257 | 2 |
| #1681 | 257 |