Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
302 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 61 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. #26022491 | C2 | semidirect |
| 3. #26019767 | C2 | semidirect |
| 4. #26018296 | C2 | semidirect |
| 5. #26018233 | C2 | semidirect |
| 6. #26018219 | C2 | semidirect |
| 7. C89×#2226 | C2 | semidirect |
| 151. #2226 | D89 | semidirect |
| 156. C89 | #12390 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033338 | 2 |
| #26022491 | 2 |
| #26019767 | 2 |
| #26018296 | 2 |
| #26018233 | 2 |
| #26018219 | 2 |
| C89×#2226 | 2 |
| #12390 | 89 |