Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
456 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 2. #26023357 | C2 | semidirect |
| 3. #26018878 | C2 | semidirect |
| 6. #26018146 | C2 | semidirect |
| 7. C89×#1300 | C2 | semidirect |
| 10. #19151967 | C4 | semidirect |
| 11. #19151963 | C4 | semidirect |
| 196. #1300 | D89 | semidirect |
| 197. C89 | #9442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030653 | 2 |
| #26023357 | 2 |
| #26018878 | 2 |
| #26018761 | 2 |
| #26018759 | 2 |
| #26018146 | 2 |
| C89×#1300 | 2 |
| #9442 | 89 |