Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
600 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 83 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 |
|---|---|---|
| 3. #26024535 | C2 | semidirect |
| 5. #26018581 | C2 | semidirect |
| 6. #26018105 | C2 | semidirect |
| 7. C89×#1826 | C2 | semidirect |
| 222. #1826 | D89 | semidirect |
| 226. C89 | #9941 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030192 | 2 |
| #26025727 | 2 |
| #26024535 | 2 |
| #26018782 | 2 |
| #26018581 | 2 |
| #26018105 | 2 |
| C89×#1826 | 2 |
| #9941 | 89 |