Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
450 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 113 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. #26020389 | C2 | semidirect |
| 3. #26018937 | C2 | semidirect |
| 6. #26018536 | C2 | semidirect |
| 7. C89×#1548 | C2 | semidirect |
| 152. #1548 | D89 | semidirect |
| 156. C89 | #9769 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151946 | 2 |
| #26020389 | 2 |
| #26018937 | 2 |
| #26018921 | 2 |
| #26018919 | 2 |
| #26018536 | 2 |
| C89×#1548 | 2 |
| #9769 | 89 |