Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
648 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26021218 | C2 | semidirect |
| 2. #26018879 | C2 | semidirect |
| 3. #26018790 | C2 | semidirect |
| 4. #26018712 | C2 | semidirect |
| 15. #564×C89 | C4 | semidirect |
| 16. #563×C89 | C4 | semidirect |
| 17. #562×C89 | C4 | semidirect |
| 185. C89 | #8529 | semidirect |
| 186. #564 | Dic89 | semidirect |
| 187. #563 | Dic89 | semidirect |
| 188. #562 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021218 | 2 |
| #26018879 | 2 |
| #26018790 | 2 |
| #26018712 | 2 |
| C89×#3553 | 2 |
| #8529 | 89 |