Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
500 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26019985 | C2 | semidirect |
| 2. #26018586 | C2 | semidirect |
| 3. #26018276 | C2 | semidirect |
| 12. C2×C4×D4×C89 | C4 | semidirect |
| 14. #400×C89 | C4 | semidirect |
| 16. #394×C89 | C4 | semidirect |
| 22. #383×C89 | C4 | semidirect |
| 200. C89 | #11754 | semidirect |
| 201. C2×C4×D4 | Dic89 | semidirect |
| 205. #400 | Dic89 | semidirect |
| 207. #394 | Dic89 | semidirect |
| 213. #383 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26019985 | 2 |
| #26018586 | 2 |
| #26018276 | 2 |
| #26018249 | 2 |
| C89×#2598 | 2 |
| #11754 | 89 |