Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
610 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 610 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 |
|---|---|---|
| 1. #26022855 | C2 | semidirect |
| 2. #26020332 | C2 | semidirect |
| 4. #26018105 | C2 | semidirect |
| 18. #390×C89 | C4 | semidirect |
| 19. #384×C89 | C4 | semidirect |
| 166. C89 | #9464 | semidirect |
| 173. #390 | Dic89 | semidirect |
| 175. #384 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022855 | 2 |
| #26020332 | 2 |
| #26018781 | 2 |
| #26018105 | 2 |
| C89×#2501 | 2 |
| #9464 | 89 |