Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
464 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 131 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. #26022462 | C2 | semidirect |
| 3. #26022456 | C2 | semidirect |
| 4. #26022413 | C2 | semidirect |
| 5. #26022361 | C2 | semidirect |
| 6. C4×Dic712 | C2 | semidirect |
| 8. #26022039 | C2 | semidirect |
| 9. C89×#2253 | C2 | semidirect |
| 134. #2253 | D89 | semidirect |
| 142. C89 | #33919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26032619 | 2 |
| #26022462 | 2 |
| #26022456 | 2 |
| #26022413 | 2 |
| #26022361 | 2 |
| C4×Dic712 | 2 |
| #26022085 | 2 |
| #26022039 | 2 |
| C89×#2253 | 2 |
| #33919 | 89 |