Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1082 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 163 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. #26034657 | C2 | semidirect |
| 2. #26031630 | C2 | semidirect |
| 3. #26019395 | C2 | semidirect |
| 4. #26019366 | C2 | semidirect |
| 5. #26019333 | C2 | semidirect |
| 6. #26019304 | C2 | semidirect |
| 7. #26018987 | C2 | semidirect |
| 8. #26018704 | C2 | semidirect |
| 9. C89×#3147 | C2 | semidirect |
| 19. #19151885 | C22 | semidirect |
| 22. #19151790 | C22 | semidirect |
| 23. #19151622 | C22 | semidirect |
| 24. #19151347 | C22 | semidirect |
| 26. #19151327 | C22 | semidirect |
| 27. #19151327 | C22 | semidirect |
| 30. #532×C89 | C22 | semidirect |
| 32. #494×C89 | C22 | semidirect |
| 35. #492×C89 | C22 | semidirect |
| 36. C2×C4×C8×C89 | C22 | semidirect |
| 208. #3147 | D89 | semidirect |
| 215. C89 | #18686 | semidirect |
| 226. #532 | C2×D89 | semidirect |
| 228. #494 | C2×D89 | semidirect |
| 231. #492 | C2×D89 | semidirect |
| 238. C2×C4×C8 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034657 | 2 |
| #26031630 | 2 |
| #26019395 | 2 |
| #26019366 | 2 |
| #26019333 | 2 |
| #26019304 | 2 |
| #26018987 | 2 |
| #26018704 | 2 |
| C89×#3147 | 2 |
| #18686 | 89 |