Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
488 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 488 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. #26032653 | C2 | semidirect |
| 2. #26022446 | C2 | semidirect |
| 3. #26022434 | C2 | semidirect |
| 4. #26022406 | C2 | semidirect |
| 5. #26022356 | C2 | semidirect |
| 6. C4×D1424 | C2 | semidirect |
| 7. #26022085 | C2 | semidirect |
| 8. #26022039 | C2 | semidirect |
| 9. C89×#2253 | C2 | semidirect |
| 140. #2253 | D89 | semidirect |
| 148. C89 | #33922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26032653 | 2 |
| #26022446 | 2 |
| #26022434 | 2 |
| #26022406 | 2 |
| #26022356 | 2 |
| C4×D1424 | 2 |
| #26022085 | 2 |
| #26022039 | 2 |
| C89×#2253 | 2 |
| #33922 | 89 |