Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26018566 | C2 | semidirect |
| 3. #26018252 | C2 | semidirect |
| 13. C2×C4×D4×C89 | C4 | semidirect |
| 15. #398×C89 | C4 | semidirect |
| 19. #394×C89 | C4 | semidirect |
| 21. C4×C4⋊C4×C89 | C4 | semidirect |
| 206. C89 | #11691 | semidirect |
| 208. C2×C4×D4 | Dic89 | semidirect |
| 212. #398 | Dic89 | semidirect |
| 216. #394 | Dic89 | semidirect |
| 218. C4×C4⋊C4 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26019985 | 2 |
| #26018566 | 2 |
| #26018252 | 2 |
| #26018249 | 2 |
| C89×#2392 | 2 |
| #11691 | 89 |