Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
472 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 139 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. #26033116 | C2 | semidirect |
| 2. #26022537 | C2 | semidirect |
| 3. #26022412 | C2 | semidirect |
| 4. #26022406 | C2 | semidirect |
| 5. #26022388 | C2 | semidirect |
| 6. #26022160 | C2 | semidirect |
| 9. C89×#2253 | C2 | semidirect |
| 46. D1424 | Q8 | semidirect |
| 133. #2253 | D89 | semidirect |
| 140. C89 | #33956 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033116 | 2 |
| #26022537 | 2 |
| #26022412 | 2 |
| #26022406 | 2 |
| #26022388 | 2 |
| #26022160 | 2 |
| #26022127 | 2 |
| C4×D1424 | 2 |
| C89×#2253 | 2 |
| #33956 | 89 |