Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
400 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26022055 | C2 | semidirect |
| 3. #26018300 | C2 | semidirect |
| 4. #26018297 | C2 | semidirect |
| 5. C89×#1567 | C2 | semidirect |
| 134. #1567 | D89 | semidirect |
| 137. C89 | #11966 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030680 | 2 |
| #26022055 | 2 |
| #26018300 | 2 |
| #26018297 | 2 |
| C89×#1567 | 2 |
| #11966 | 89 |