Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
306 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 1. #26022017 | C2 | semidirect |
| 5. #26021033 | C2 | semidirect |
| 6. #26018357 | C2 | semidirect |
| 7. C89×#2155 | C2 | semidirect |
| 140. #2155 | D89 | semidirect |
| 147. C89 | #13469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022017 | 2 |
| C2×#19151409 | 2 |
| #26021979 | 2 |
| #26021148 | 2 |
| #26021033 | 2 |
| #26018357 | 2 |
| C89×#2155 | 2 |
| #13469 | 89 |