Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
392 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26022008 | C2 | semidirect |
| 3. #26022001 | C2 | semidirect |
| 4. #26021999 | C2 | semidirect |
| 5. #26021140 | C2 | semidirect |
| 6. #26018355 | C2 | semidirect |
| 7. C89×#1974 | C2 | semidirect |
| 187. #1974 | D89 | semidirect |
| 189. C89 | #13444 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033386 | 2 |
| #26022008 | 2 |
| #26022001 | 2 |
| #26021999 | 2 |
| #26021140 | 2 |
| #26018355 | 2 |
| C89×#1974 | 2 |
| #13444 | 89 |