Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
472 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 472 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 |
|---|---|---|
| 3. #26018252 | C2 | semidirect |
| 13. C22×C4⋊C4×C89 | C4 | semidirect |
| 14. #398×C89 | C4 | semidirect |
| 19. #380×C89 | C4 | semidirect |
| 170. C89 | #11874 | semidirect |
| 173. C22×C4⋊C4 | Dic89 | semidirect |
| 176. #398 | Dic89 | semidirect |
| 182. #380 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020240 | 2 |
| #26018573 | 2 |
| #26018252 | 2 |
| C89×#2486 | 2 |
| #11874 | 89 |