Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1082 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 179 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. #26031630 | C2 | semidirect |
| 2. #26030678 | C2 | semidirect |
| 3. #26019397 | C2 | semidirect |
| 4. #26019368 | C2 | semidirect |
| 5. #26019335 | C2 | semidirect |
| 6. #26019306 | C2 | semidirect |
| 7. #26018987 | C2 | semidirect |
| 8. #26018703 | C2 | semidirect |
| 9. C89×#3549 | C2 | semidirect |
| 11. #19152148 | C22 | semidirect |
| 13. #19151977 | C22 | semidirect |
| 15. #19151972 | C22 | semidirect |
| 17. #19151888 | C22 | semidirect |
| 20. #19151793 | C22 | semidirect |
| 22. #19151622 | C22 | semidirect |
| 23. C2×C4×#10623494 | C22 | semidirect |
| 24. #19151347 | C22 | semidirect |
| 26. D4⋊#10623494 | C22 | semidirect |
| 27. D4⋊#10623494 | C22 | semidirect |
| 206. #3549 | D89 | semidirect |
| 215. C89 | #18686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031630 | 2 |
| #26030678 | 2 |
| #26019397 | 2 |
| #26019368 | 2 |
| #26019335 | 2 |
| #26019306 | 2 |
| #26018987 | 2 |
| #26018703 | 2 |
| C89×#3549 | 2 |
| #18686 | 89 |