Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
574 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26022615 | C2 | semidirect |
| 5. #26018700 | C2 | semidirect |
| 6. #26018109 | C2 | semidirect |
| 7. C89×#1300 | C2 | semidirect |
| 12. #19151894 | C4 | semidirect |
| 13. #19151799 | C4 | semidirect |
| 153. Dic178 | #104 | semidirect |
| 189. #1300 | D89 | semidirect |
| 191. C89 | #9326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030375 | 2 |
| #26022615 | 2 |
| #26021171 | 2 |
| #26018759 | 2 |
| #26018700 | 2 |
| #26018109 | 2 |
| C89×#1300 | 2 |
| #9326 | 89 |