Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
318 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26018235 | C2 | semidirect |
| 4. #26018211 | C2 | semidirect |
| 5. C4×M32×C89 | C2 | semidirect |
| 141. C4×M32 | D89 | semidirect |
| 144. C89 | #11620 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029227 | 2 |
| #26022055 | 2 |
| #26018235 | 2 |
| #26018211 | 2 |
| C4×M32×C89 | 2 |
| #11620 | 89 |