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. #26030998 | C2 | semidirect |
| 2. #26030973 | C2 | semidirect |
| 4. #26030623 | C2 | semidirect |
| 5. #26019921 | C2 | semidirect |
| 6. #26019906 | C2 | semidirect |
| 7. #26019892 | C2 | semidirect |
| 8. #26019881 | C2 | semidirect |
| 9. #26019858 | C2 | semidirect |
| 10. #26018554 | C2 | semidirect |
| 11. C89×#1708 | C2 | semidirect |
| 16. #19152001 | C22 | semidirect |
| 18. #19151978 | C22 | semidirect |
| 22. #19151972 | C22 | semidirect |
| 24. #19151950 | C22 | semidirect |
| 27. #19151945 | C22 | semidirect |
| 36. #19151319 | C22 | semidirect |
| 37. #19151319 | C22 | semidirect |
| 38. #498×C89 | C22 | semidirect |
| 40. #487×C89 | C22 | semidirect |
| 42. C82×C89 | C22 | semidirect |
| 197. #1708 | D89 | semidirect |
| 199. C89 | #19749 | semidirect |
| 205. #498 | C2×D89 | semidirect |
| 215. #487 | 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 |
|---|---|
| #26030998 | 2 |
| #26030973 | 2 |
| #26030699 | 2 |
| #26030623 | 2 |
| #26019921 | 2 |
| #26019906 | 2 |
| #26019892 | 2 |
| #26019881 | 2 |
| #26019858 | 2 |
| #26018554 | 2 |
| C89×#1708 | 2 |
| #19749 | 89 |