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. #26030968 | C2 | semidirect |
| 4. #26030623 | C2 | semidirect |
| 5. #26019923 | C2 | semidirect |
| 6. #26019904 | C2 | semidirect |
| 7. #26019889 | C2 | semidirect |
| 8. #26019857 | C2 | semidirect |
| 9. #26019854 | C2 | semidirect |
| 10. #26018556 | C2 | semidirect |
| 11. C89×#1715 | C2 | semidirect |
| 16. #19152003 | C22 | semidirect |
| 18. #19151978 | C22 | semidirect |
| 23. #19151950 | C22 | semidirect |
| 24. #19151948 | C22 | semidirect |
| 28. #19151944 | C22 | semidirect |
| 36. #19151320 | C22 | semidirect |
| 37. C8×#10623494 | C22 | semidirect |
| 38. #498×C89 | C22 | semidirect |
| 40. #492×C89 | C22 | semidirect |
| 42. #322×C89 | C22 | semidirect |
| 195. #1715 | D89 | semidirect |
| 199. C89 | #19749 | semidirect |
| 205. #498 | C2×D89 | semidirect |
| 212. #492 | C2×D89 | semidirect |
| 229. #322 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030998 | 2 |
| #26030968 | 2 |
| #26030703 | 2 |
| #26030623 | 2 |
| #26019923 | 2 |
| #26019904 | 2 |
| #26019889 | 2 |
| #26019857 | 2 |
| #26019854 | 2 |
| #26018556 | 2 |
| C89×#1715 | 2 |
| #19749 | 89 |