Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
582 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 582 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. #26029281 | C2 | semidirect |
| 2. C4×#15667927 | C2 | semidirect |
| 3. #26018768 | C2 | semidirect |
| 4. #26018104 | C2 | semidirect |
| 16. #400×C89 | C4 | semidirect |
| 17. #399×C89 | C4 | semidirect |
| 19. #394×C89 | C4 | semidirect |
| 21. #392×C89 | C4 | semidirect |
| 33. C22⋊#10623494 | D4 | semidirect |
| 209. C89 | #9185 | semidirect |
| 217. #400 | Dic89 | semidirect |
| 218. #399 | Dic89 | semidirect |
| 220. #394 | Dic89 | semidirect |
| 222. #392 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029281 | 2 |
| C4×#15667927 | 2 |
| #26018768 | 2 |
| #26018104 | 2 |
| C89×#2635 | 2 |
| #9185 | 89 |