Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
680 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 3. #26029120 | C2 | semidirect |
| 4. #26022316 | C2 | semidirect |
| 5. #26022300 | C2 | semidirect |
| 6. #26022010 | C2 | semidirect |
| 7. #26021972 | C2 | semidirect |
| 9. C22×Q32×C89 | C2 | semidirect |
| 173. C22×Q32 | D89 | semidirect |
| 181. C89 | #33588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152039 | 2 |
| #26030741 | 2 |
| #26029120 | 2 |
| #26022316 | 2 |
| #26022300 | 2 |
| #26022010 | 2 |
| #26021972 | 2 |
| #26021960 | 2 |
| C22×Q32×C89 | 2 |
| #33588 | 89 |