Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
688 conjugacy classes of subgroups; only the 215 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 215 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. #26020748 | C2 | semidirect |
| 2. #26020727 | C2 | semidirect |
| 3. #26020646 | C2 | semidirect |
| 5. #26020401 | C2 | semidirect |
| 20. #497×C89 | C4 | semidirect |
| 21. #494×C89 | C4 | semidirect |
| 22. #492×C89 | C4 | semidirect |
| 134. C89 | #23360 | semidirect |
| 140. #497 | Dic89 | semidirect |
| 141. #494 | Dic89 | semidirect |
| 142. #492 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26020748 | 2 |
| #26020727 | 2 |
| #26020646 | 2 |
| #26020636 | 2 |
| #26020401 | 2 |
| C89×#3152 | 2 |
| #23360 | 89 |