Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
822 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 159 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. #26030995 | C2 | semidirect |
| 2. #26030969 | C2 | semidirect |
| 4. #26030623 | C2 | semidirect |
| 5. #26019924 | C2 | semidirect |
| 6. #26019902 | C2 | semidirect |
| 7. #26019888 | C2 | semidirect |
| 8. #26019878 | C2 | semidirect |
| 9. #26019853 | C2 | semidirect |
| 10. #26018554 | C2 | semidirect |
| 11. C89×#1709 | C2 | semidirect |
| 16. #19152001 | C22 | semidirect |
| 17. #19151996 | C22 | semidirect |
| 22. #19151970 | C22 | semidirect |
| 24. #19151949 | C22 | semidirect |
| 25. #19151948 | C22 | semidirect |
| 36. #19151319 | C22 | semidirect |
| 37. #19151319 | C22 | semidirect |
| 38. #494×C89 | C22 | semidirect |
| 41. #486×C89 | C22 | semidirect |
| 42. C82×C89 | C22 | semidirect |
| 196. #1709 | D89 | semidirect |
| 199. C89 | #19749 | semidirect |
| 207. #494 | C2×D89 | semidirect |
| 220. #486 | C2×D89 | semidirect |
| 230. C82 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030995 | 2 |
| #26030969 | 2 |
| #26030703 | 2 |
| #26030623 | 2 |
| #26019924 | 2 |
| #26019902 | 2 |
| #26019888 | 2 |
| #26019878 | 2 |
| #26019853 | 2 |
| #26018554 | 2 |
| C89×#1709 | 2 |
| #19749 | 89 |