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 |
|---|---|---|
| 1. #26028863 | C2 | semidirect |
| 2. #26022464 | C2 | semidirect |
| 3. #26022024 | C2 | semidirect |
| 4. C2×#19151411 | C2 | semidirect |
| 5. #26021873 | C2 | semidirect |
| 10. #19151647 | C22 | semidirect |
| 13. #19151420 | C22 | semidirect |
| 15. #19151380 | C22 | semidirect |
| 137. C89 | #33657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028863 | 2 |
| #26022464 | 2 |
| #26022024 | 2 |
| C2×#19151411 | 2 |
| #26021873 | 2 |
| C89×#3058 | 2 |
| #33657 | 89 |