Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
464 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 127 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. #26022419 | C2 | semidirect |
| 3. #26022414 | C2 | semidirect |
| 6. #26022301 | C2 | semidirect |
| 7. #26022300 | C2 | semidirect |
| 147. C89 | #33827 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030904 | 2 |
| #26022419 | 2 |
| #26022414 | 2 |
| #26022360 | 2 |
| #26022341 | 2 |
| #26022301 | 2 |
| #26022300 | 2 |
| #26022012 | 2 |
| C89×#2219 | 2 |
| #33827 | 89 |