Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
492 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26021197 | C2 | semidirect |
| 3. #26018764 | C2 | semidirect |
| 5. #26018144 | C2 | semidirect |
| 6. #26018109 | C2 | semidirect |
| 24. #474×C89 | C4 | semidirect |
| 25. #461×C89 | C4 | semidirect |
| 189. C89 | #9327 | semidirect |
| 193. #474 | Dic89 | semidirect |
| 194. #461 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022895 | 2 |
| #26021197 | 2 |
| #26018764 | 2 |
| #26018695 | 2 |
| #26018144 | 2 |
| #26018109 | 2 |
| C89×#3110 | 2 |
| #9327 | 89 |