Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
528 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26033264 | C2 | semidirect |
| 2. #26022515 | C2 | semidirect |
| 3. #26022513 | C2 | semidirect |
| 4. #26022313 | C2 | semidirect |
| 5. #26022307 | C2 | semidirect |
| 6. #26022286 | C2 | semidirect |
| 7. #26022160 | C2 | semidirect |
| 8. #26022115 | C2 | semidirect |
| 9. C4×D16×C89 | C2 | semidirect |
| 158. C4×D16 | D89 | semidirect |
| 159. C89 | #33970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033264 | 2 |
| #26022515 | 2 |
| #26022513 | 2 |
| #26022313 | 2 |
| #26022307 | 2 |
| #26022286 | 2 |
| #26022160 | 2 |
| #26022115 | 2 |
| C4×D16×C89 | 2 |
| #33970 | 89 |