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 |
| 4. #26019331 | C2 | direct (N × H) |
| 5. C2×#19151328 | C2 | semidirect |
| 6. C2×#333×C89 | C2 | semidirect |
| 11. #19152328 | C22 | semidirect |
| 23. #19151328 | C22 | semidirect |
| 26. #333×C89 | C22 | semidirect |
| 71. C2×Dic178 | SD16 | semidirect |
| 134. Dic178 | C2×SD16 | semidirect |
| 152. C2×C89 | #1623 | semidirect |
| 160. C2×#333 | D89 | semidirect |
| 162. C89 | C2×#1623 | semidirect |
| 181. #333 | C2×D89 | semidirect |
| 308. C2 | #26019331 | 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×#19151972 | 2 |
| C2×#19151799 | 2 |
| #26019331 | 2 |
| C2×#19151328 | 2 |
| C2×#333×C89 | 2 |
| C2×#1623 | 89 |