Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1198 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1198 conjugacy classes of subgroups — too many to draw. Only its 183 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. #26030339 | C2 | semidirect |
| 2. #26023535 | C2 | semidirect |
| 3. #26019289 | C2 | semidirect |
| 4. #26019187 | C2 | semidirect |
| 5. #26018760 | C2 | semidirect |
| 6. #26018596 | C2 | semidirect |
| 7. C89×#3497 | C2 | semidirect |
| 199. #3497 | D89 | semidirect |
| 206. C89 | #18186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030339 | 2 |
| #26023535 | 2 |
| #26019289 | 2 |
| #26019187 | 2 |
| #26018760 | 2 |
| #26018596 | 2 |
| C89×#3497 | 2 |
| #18186 | 89 |