Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1256 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1256 conjugacy classes of subgroups — too many to draw. Only its 167 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. C2×#19152179 | C2 | semidirect |
| 2. #26031049 | C2 | semidirect |
| 3. #26019288 | C2 | semidirect |
| 4. #26019186 | C2 | semidirect |
| 5. #26018767 | C2 | semidirect |
| 6. #26018582 | C2 | semidirect |
| 7. C89×#2591 | C2 | semidirect |
| 16. #19151916 | C22 | semidirect |
| 19. #19151732 | C22 | semidirect |
| 22. #19151331 | C22 | semidirect |
| 23. #19151324 | C22 | semidirect |
| 26. #400×C89 | C22 | semidirect |
| 27. #394×C89 | C22 | semidirect |
| 225. #2591 | D89 | semidirect |
| 230. C89 | #18324 | semidirect |
| 247. #400 | C2×D89 | semidirect |
| 248. #394 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152179 | 2 |
| #26031049 | 2 |
| #26019288 | 2 |
| #26019186 | 2 |
| #26018767 | 2 |
| #26018582 | 2 |
| C89×#2591 | 2 |
| #18324 | 89 |