Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
792 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26025982 | C2 | semidirect |
| 3. #26021089 | C2 | semidirect |
| 4. #26020195 | C2 | semidirect |
| 5. #26018772 | C2 | semidirect |
| 6. #26018157 | C2 | semidirect |
| 7. C89×#3193 | C2 | semidirect |
| 269. #3193 | D89 | semidirect |
| 276. C89 | #9931 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029502 | 2 |
| #26025982 | 2 |
| #26021089 | 2 |
| #26020195 | 2 |
| #26018772 | 2 |
| #26018157 | 2 |
| C89×#3193 | 2 |
| #9931 | 89 |