Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1166 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1166 conjugacy classes of subgroups — too many to draw. Only its 167 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. #26030374 | C2 | semidirect |
| 3. #26019254 | C2 | semidirect |
| 4. #26019220 | C2 | semidirect |
| 5. #26018759 | C2 | semidirect |
| 6. #26018596 | C2 | semidirect |
| 7. C89×#2399 | C2 | semidirect |
| 191. #2399 | D89 | semidirect |
| 196. C89 | #18187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034023 | 2 |
| #26030374 | 2 |
| #26019254 | 2 |
| #26019220 | 2 |
| #26018759 | 2 |
| #26018596 | 2 |
| C89×#2399 | 2 |
| #18187 | 89 |