Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1328 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 251 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. #26034964 | C2 | semidirect |
| 3. #26028949 | C2 | semidirect |
| 4. #26020668 | C2 | semidirect |
| 5. #26020537 | C2 | semidirect |
| 6. #26020055 | C2 | semidirect |
| 7. C89×#1791 | C2 | semidirect |
| 12. C22×C8×D89 | C22 | semidirect |
| 18. #19151624 | C22 | semidirect |
| 20. #19151561 | C22 | semidirect |
| 21. #19151556 | C22 | semidirect |
| 22. #19151370 | C22 | semidirect |
| 34. C2×#13083558 | D4 | semidirect |
| 37. C22×#10623494 | D4 | semidirect |
| 150. #1791 | D89 | semidirect |
| 152. C89 | #21483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034964 | 2 |
| #26029644 | 2 |
| #26028949 | 2 |
| #26020668 | 2 |
| #26020537 | 2 |
| #26020055 | 2 |
| C89×#1791 | 2 |
| #21483 | 89 |