Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
396 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26021873 | C2 | semidirect |
| 2. #26020298 | C2 | semidirect |
| 3. #26018237 | C2 | semidirect |
| 9. #19151380 | C22 | semidirect |
| 10. #19151355 | C22 | semidirect |
| 11. C22×D8×C89 | C4 | semidirect |
| 14. #469×C89 | C4 | semidirect |
| 18. #427×C89 | C4 | semidirect |
| 155. C89 | #11868 | semidirect |
| 156. C22×D8 | Dic89 | semidirect |
| 160. #469 | Dic89 | semidirect |
| 165. #427 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021873 | 2 |
| #26020298 | 2 |
| #26018237 | 2 |
| C89×#3058 | 2 |
| #11868 | 89 |