Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
996 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 996 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 |
|---|---|---|
| 2. #26031635 | C2 | semidirect |
| 3. #26019477 | C2 | semidirect |
| 4. #26019428 | C2 | semidirect |
| 5. #26018987 | C2 | semidirect |
| 6. #26018704 | C2 | semidirect |
| 7. C89×#3131 | C2 | semidirect |
| 17. #19151875 | C22 | semidirect |
| 19. #19151800 | C22 | semidirect |
| 21. #19151622 | C22 | semidirect |
| 22. #19151347 | C22 | semidirect |
| 24. #19151327 | C22 | semidirect |
| 25. #533×C89 | C22 | semidirect |
| 28. #487×C89 | C22 | semidirect |
| 31. C2×C4×C8×C89 | C22 | semidirect |
| 182. #3131 | D89 | semidirect |
| 187. C89 | #18691 | semidirect |
| 195. #533 | C2×D89 | semidirect |
| 199. #487 | C2×D89 | semidirect |
| 208. 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 |
| #26031635 | 2 |
| #26019477 | 2 |
| #26019428 | 2 |
| #26018987 | 2 |
| #26018704 | 2 |
| C89×#3131 | 2 |
| #18691 | 89 |