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. #26022616 | C2 | semidirect |
| 5. #26018698 | C2 | semidirect |
| 6. #26018144 | C2 | semidirect |
| 7. C89×#1285 | C2 | semidirect |
| 12. #19151894 | C4 | semidirect |
| 13. #19151799 | C4 | semidirect |
| 153. Dic178 | #104 | semidirect |
| 190. #1285 | 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 |
| #26022616 | 2 |
| #26021170 | 2 |
| #26018761 | 2 |
| #26018698 | 2 |
| #26018144 | 2 |
| C89×#1285 | 2 |
| #9326 | 89 |