Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
256 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 63 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. #26022400 | C2 | semidirect |
| 3. #26019841 | C2 | semidirect |
| 4. #26019046 | C2 | semidirect |
| 5. #26018315 | C2 | semidirect |
| 6. #26018311 | C2 | semidirect |
| 7. C89×#1361 | C2 | semidirect |
| 50. D712 | SD16 | semidirect |
| 121. #1361 | D89 | semidirect |
| 122. C89 | #12418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022400 | 2 |
| #26022284 | 2 |
| #26019841 | 2 |
| #26019046 | 2 |
| #26018315 | 2 |
| #26018311 | 2 |
| C89×#1361 | 2 |
| #12418 | 89 |