Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
748 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 748 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. C2×#19152036 | C2 | semidirect |
| 2. C22×#15667953 | C2 | semidirect |
| 3. #26030733 | C2 | semidirect |
| 4. #26029103 | C2 | semidirect |
| 5. #26022306 | C2 | semidirect |
| 6. #26022286 | C2 | semidirect |
| 7. #26022012 | C2 | semidirect |
| 8. #26021957 | C2 | semidirect |
| 9. C89×#2140 | C2 | semidirect |
| 16. C2×#15667957 | C22 | semidirect |
| 17. C2×D1424 | C22 | semidirect |
| 22. #19151981 | C22 | semidirect |
| 23. #19151973 | C22 | semidirect |
| 25. #19151680 | C22 | semidirect |
| 28. #19151416 | C22 | semidirect |
| 29. #19151401 | C22 | semidirect |
| 30. #19151398 | C22 | semidirect |
| 34. #357×C89 | C22 | semidirect |
| 45. C2×D712 | D4 | semidirect |
| 189. #2140 | D89 | semidirect |
| 191. C89 | #33585 | semidirect |
| 216. #357 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152036 | 2 |
| C22×#15667953 | 2 |
| #26030733 | 2 |
| #26029103 | 2 |
| #26022306 | 2 |
| #26022286 | 2 |
| #26022012 | 2 |
| #26021957 | 2 |
| C89×#2140 | 2 |
| #33585 | 89 |