Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
324 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26022051 | C2 | semidirect |
| 2. #26020383 | C2 | semidirect |
| 3. #26018264 | C2 | semidirect |
| 13. #499×C89 | C4 | semidirect |
| 14. #495×C89 | C4 | semidirect |
| 19. C4×Q16×C89 | C4 | semidirect |
| 21. C4×D8×C89 | C4 | semidirect |
| 147. C89 | #11855 | semidirect |
| 149. #499 | Dic89 | semidirect |
| 150. #495 | Dic89 | semidirect |
| 155. C4×Q16 | Dic89 | semidirect |
| 157. C4×D8 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022051 | 2 |
| #26020383 | 2 |
| #26018264 | 2 |
| #26018261 | 2 |
| C89×#3168 | 2 |
| #11855 | 89 |