Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
334 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 107 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. #26021851 | C2 | semidirect |
| 4. #26021038 | C2 | semidirect |
| 5. #26018361 | C2 | semidirect |
| 6. #26018345 | C2 | semidirect |
| 23. #361×C89 | C4 | semidirect |
| 152. C89 | #13144 | semidirect |
| 163. #361 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151399 | 2 |
| #26021851 | 2 |
| #26021163 | 2 |
| #26021038 | 2 |
| #26018361 | 2 |
| #26018345 | 2 |
| C2×#361×C89 | 2 |
| #13144 | 89 |