Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
392 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 91 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. #26020302 | C2 | semidirect |
| 3. #26018244 | C2 | semidirect |
| 4. C89×#2115 | C2 | semidirect |
| 15. #19151356 | C22 | semidirect |
| 19. #349×C89 | C22 | semidirect |
| 151. #2115 | D89 | semidirect |
| 154. C89 | #11870 | semidirect |
| 168. #349 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029900 | 2 |
| #26020302 | 2 |
| #26018244 | 2 |
| C89×#2115 | 2 |
| #11870 | 89 |