Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
378 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 115 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. #26022051 | C2 | semidirect |
| 3. #26018260 | C2 | semidirect |
| 4. C89×#1834 | C2 | semidirect |
| 6. #19152003 | C4 | semidirect |
| 7. #19151975 | C4 | semidirect |
| 12. C4×D712 | C4 | semidirect |
| 133. #1834 | D89 | semidirect |
| 135. C89 | #11856 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030831 | 2 |
| #26022051 | 2 |
| #26018260 | 2 |
| C89×#1834 | 2 |
| #11856 | 89 |