Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1126 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1126 conjugacy classes of subgroups — too many to draw. Only its 219 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. C2×#19152328 | C2 | semidirect |
| 3. #26019328 | C2 | direct (N × H) |
| 4. C2×#19151347 | C2 | semidirect |
| 5. C2×#19151330 | C2 | semidirect |
| 10. #19152328 | C22 | semidirect |
| 19. #19151347 | C22 | semidirect |
| 20. #19151330 | C22 | semidirect |
| 70. C2×Dic178 | SD16 | semidirect |
| 134. Dic178 | C2×SD16 | semidirect |
| 153. C2×C89 | #1623 | semidirect |
| 162. C89 | C2×#1623 | semidirect |
| 308. C2 | #26019328 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152328 | 2 |
| C2×#19151795 | 2 |
| #26019328 | 2 |
| C2×#19151347 | 2 |
| C2×#19151330 | 2 |
| C2×#492×C89 | 2 |
| C2×#1623 | 89 |