Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
556 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26021827 | C2 | semidirect |
| 2. #26021427 | C2 | semidirect |
| 3. #26021423 | C2 | semidirect |
| 4. #26021227 | C2 | semidirect |
| 7. #26020495 | C2 | semidirect |
| 8. #26020489 | C2 | semidirect |
| 9. C89×#2102 | C2 | semidirect |
| 36. #15668012 | Q8 | semidirect |
| 38. #15668009 | Q8 | semidirect |
| 40. #15668000 | Q8 | semidirect |
| 157. #2102 | D89 | semidirect |
| 165. C89 | #32704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021827 | 2 |
| #26021427 | 2 |
| #26021423 | 2 |
| #26021227 | 2 |
| #26021079 | 2 |
| #26020634 | 2 |
| #26020495 | 2 |
| #26020489 | 2 |
| C89×#2102 | 2 |
| #32704 | 89 |