Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
642 conjugacy classes of subgroups; only the 207 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 207 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. #26029168 | C2 | semidirect |
| 3. #26022137 | C2 | semidirect |
| 4. #26022132 | C2 | semidirect |
| 5. C2×#19151404 | C2 | semidirect |
| 6. #26021851 | C2 | semidirect |
| 7. C89×#2161 | C2 | semidirect |
| 10. #19152041 | C4 | semidirect |
| 11. #19152036 | C4 | semidirect |
| 15. #19151714 | C22 | semidirect |
| 18. #19151404 | C22 | semidirect |
| 19. #19151404 | C22 | semidirect |
| 20. #19151373 | C22 | semidirect |
| 21. C16×Dic89 | C22 | semidirect |
| 24. #368×C89 | C22 | semidirect |
| 125. #2161 | D89 | semidirect |
| 128. C89 | #33464 | semidirect |
| 141. #368 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033388 | 2 |
| #26029168 | 2 |
| #26022137 | 2 |
| #26022132 | 2 |
| C2×#19151404 | 2 |
| #26021851 | 2 |
| C89×#2161 | 2 |
| #33464 | 89 |