Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1090 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 183 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 |
|---|---|---|
| 2. C2×#19152039 | C2 | semidirect |
| 3. #26022202 | C2 | semidirect |
| 4. #26021987 | C2 | semidirect |
| 5. #26021873 | C2 | semidirect |
| 6. C89×#3059 | C2 | semidirect |
| 16. #19152039 | C22 | semidirect |
| 19. C2×#15667952 | C22 | semidirect |
| 20. #19151407 | C22 | semidirect |
| 21. #19151380 | C22 | semidirect |
| 22. C22×Q16×C89 | C22 | semidirect |
| 25. #470×C89 | C22 | semidirect |
| 27. #427×C89 | C22 | semidirect |
| 200. #3059 | D89 | semidirect |
| 204. C89 | #33532 | semidirect |
| 213. C22×Q16 | C2×D89 | semidirect |
| 221. #470 | C2×D89 | semidirect |
| 223. #427 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26035026 | 2 |
| C2×#19152039 | 2 |
| #26022202 | 2 |
| #26021987 | 2 |
| #26021873 | 2 |
| C89×#3059 | 2 |
| #33532 | 89 |