Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
530 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 155 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. #26020424 | C2 | semidirect |
| 3. #26018923 | C2 | semidirect |
| 5. C89×#1450 | C2 | semidirect |
| 121. #1450 | D89 | semidirect |
| 122. C89 | #9768 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151971 | 2 |
| #26020424 | 2 |
| #26018923 | 2 |
| #26018919 | 2 |
| C89×#1450 | 2 |
| #9768 | 89 |