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 |
|---|---|---|
| 1. #26031054 | C2 | semidirect |
| 3. #26021087 | C2 | semidirect |
| 4. #26020196 | C2 | semidirect |
| 5. #26018772 | C2 | semidirect |
| 6. #26018158 | C2 | semidirect |
| 7. C89×#2616 | C2 | semidirect |
| 271. #2616 | 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 |
|---|---|
| #26031054 | 2 |
| #26029504 | 2 |
| #26021087 | 2 |
| #26020196 | 2 |
| #26018772 | 2 |
| #26018158 | 2 |
| C89×#2616 | 2 |
| #9931 | 89 |