Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
574 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26020326 | C2 | semidirect |
| 2. #26018579 | C2 | semidirect |
| 3. #26018252 | C2 | semidirect |
| 4. #26018249 | C2 | semidirect |
| 12. C2×#121×C89 | C4 | semidirect |
| 15. #397×C89 | C4 | semidirect |
| 19. #392×C89 | C4 | semidirect |
| 22. #380×C89 | C4 | semidirect |
| 229. C89 | #11799 | semidirect |
| 230. C2×#121 | Dic89 | semidirect |
| 234. #397 | Dic89 | semidirect |
| 238. #392 | Dic89 | semidirect |
| 241. #380 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020326 | 2 |
| #26018579 | 2 |
| #26018252 | 2 |
| #26018249 | 2 |
| C89×#2617 | 2 |
| #11799 | 89 |