Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1168 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 139 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. #26020180 | C2 | semidirect |
| 2. #26020170 | C2 | semidirect |
| 3. #26018781 | C2 | semidirect |
| 9. #19151562 | C22 | semidirect |
| 10. #19151461 | C22 | semidirect |
| 13. C23×D4×C89 | C4 | semidirect |
| 17. C2×#121×C89 | C4 | semidirect |
| 21. C2×#117×C89 | C4 | semidirect |
| 213. C89 | #8516 | semidirect |
| 215. C23×D4 | Dic89 | semidirect |
| 219. C2×#121 | Dic89 | semidirect |
| 223. C2×#117 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020180 | 2 |
| #26020170 | 2 |
| #26018781 | 2 |
| C2×#535×C89 | 2 |
| #8516 | 89 |