Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1282 conjugacy classes of subgroups; only the 187 normal subgroups are shown.
This group has 1282 conjugacy classes of subgroups — too many to draw. Only its 187 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. #26031000 | C2 | semidirect |
| 3. #26019254 | C2 | semidirect |
| 4. #26019186 | C2 | semidirect |
| 5. #26018819 | C2 | semidirect |
| 6. C2×#19151324 | C2 | semidirect |
| 7. C89×#2618 | C2 | semidirect |
| 16. #19151911 | C22 | semidirect |
| 19. #19151732 | C22 | semidirect |
| 22. #19151331 | C22 | semidirect |
| 23. #19151324 | C22 | semidirect |
| 27. #398×C89 | C22 | semidirect |
| 29. #394×C89 | C22 | semidirect |
| 130. C22×C4×C89 | D8 | semidirect |
| 239. #2618 | D89 | semidirect |
| 244. C89 | #18292 | semidirect |
| 262. #398 | C2×D89 | semidirect |
| 264. #394 | C2×D89 | semidirect |
| 358. C22×C4 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152179 | 2 |
| #26031000 | 2 |
| #26019254 | 2 |
| #26019186 | 2 |
| #26018819 | 2 |
| C2×#19151324 | 2 |
| C89×#2618 | 2 |
| #18292 | 89 |