Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 2. #26022466 | C2 | semidirect |
| 3. #26022026 | C2 | semidirect |
| 4. C2×#19151410 | C2 | semidirect |
| 5. #26021873 | C2 | semidirect |
| 6. C89×#2916 | C2 | semidirect |
| 14. #19151422 | C22 | semidirect |
| 16. #19151380 | C22 | semidirect |
| 20. #430×C89 | C22 | semidirect |
| 132. #2916 | D89 | semidirect |
| 137. C89 | #33657 | semidirect |
| 146. #430 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029900 | 2 |
| #26022466 | 2 |
| #26022026 | 2 |
| C2×#19151410 | 2 |
| #26021873 | 2 |
| C89×#2916 | 2 |
| #33657 | 89 |