Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
326 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 71 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. #26022064 | C2 | semidirect |
| 3. #26018284 | C2 | semidirect |
| 4. C89×#2165 | C2 | semidirect |
| 15. #19151376 | C22 | semidirect |
| 19. #347×C89 | C22 | semidirect |
| 111. #2165 | D89 | semidirect |
| 113. C89 | #11915 | semidirect |
| 128. #347 | C2×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030627 | 2 |
| #26022064 | 2 |
| #26018284 | 2 |
| C89×#2165 | 2 |
| #11915 | 89 |