Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1136 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 1136 conjugacy classes of subgroups — too many to draw. Only its 171 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 |
|---|---|---|
| 3. #26022265 | C2 | direct (N × H) |
| 4. C2×#19151393 | C2 | semidirect |
| 5. C2×#19151388 | C2 | semidirect |
| 6. C2×#563×C89 | C2 | semidirect |
| 18. #19151393 | C22 | semidirect |
| 19. #19151388 | C22 | semidirect |
| 22. #563×C89 | C22 | semidirect |
| 225. C2×C89 | #2201 | semidirect |
| 228. C2×#563 | D89 | semidirect |
| 234. C89 | C2×#2201 | semidirect |
| 239. #563 | C2×D89 | semidirect |
| 453. C2 | #26022265 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151787 | 2 |
| C2×#19151775 | 2 |
| #26022265 | 2 |
| C2×#19151393 | 2 |
| C2×#19151388 | 2 |
| C2×#563×C89 | 2 |
| C2×#2201 | 89 |