Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
736 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 736 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. #26030997 | C2 | semidirect |
| 2. #26030993 | C2 | semidirect |
| 4. #26019914 | C2 | semidirect |
| 5. #26019913 | C2 | semidirect |
| 6. #26019911 | C2 | semidirect |
| 7. #26019863 | C2 | semidirect |
| 8. #26018555 | C2 | semidirect |
| 11. #19151996 | C22 | semidirect |
| 12. #19151994 | C22 | semidirect |
| 13. #19151978 | C22 | semidirect |
| 14. #19151977 | C22 | semidirect |
| 16. #19151950 | C22 | semidirect |
| 17. #19151949 | C22 | semidirect |
| 18. #19151948 | C22 | semidirect |
| 29. #19151320 | C22 | semidirect |
| 30. #19151319 | C22 | semidirect |
| 31. C8×#10623494 | C22 | semidirect |
| 169. C89 | #19753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030997 | 2 |
| #26030993 | 2 |
| #26030626 | 2 |
| #26019914 | 2 |
| #26019913 | 2 |
| #26019911 | 2 |
| #26019863 | 2 |
| #26018555 | 2 |
| C89×#3138 | 2 |
| #19753 | 89 |