Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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. #26022508 | C2 | semidirect |
| 2. #26022507 | C2 | semidirect |
| 3. #26022501 | C2 | semidirect |
| 4. #26019866 | C2 | semidirect |
| 5. #26019857 | C2 | semidirect |
| 6. #26018168 | C2 | semidirect |
| 7. C89×#2246 | C2 | semidirect |
| 53. #13083549 | D8 | semidirect |
| 65. C16×C89 | D8 | semidirect |
| 106. #2246 | D89 | semidirect |
| 110. C89 | #12519 | semidirect |
| 168. C16 | #13083559 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022508 | 2 |
| #26022507 | 2 |
| #26022501 | 2 |
| #26019866 | 2 |
| #26019857 | 2 |
| #26018168 | 2 |
| C89×#2246 | 2 |
| #12519 | 89 |