Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
696 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 151 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×#19152031 | C2 | semidirect |
| 2. #26032011 | C2 | semidirect |
| 3. #26022502 | C2 | semidirect |
| 4. #26022339 | C2 | semidirect |
| 5. #26022292 | C2 | semidirect |
| 6. #26022178 | C2 | semidirect |
| 7. C16×D356 | C2 | semidirect |
| 8. C4×Q32×C89 | C2 | semidirect |
| 52. Q32×C89 | D4 | semidirect |
| 124. C4×C89 | #508 | semidirect |
| 140. C4×Q32 | D89 | semidirect |
| 142. C89 | #33853 | semidirect |
| 178. Q32 | D356 | semidirect |
| 259. C4 | #19152031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152031 | 2 |
| #26032011 | 2 |
| #26022502 | 2 |
| #26022339 | 2 |
| #26022292 | 2 |
| #26022178 | 2 |
| C16×D356 | 2 |
| C4×Q32×C89 | 2 |
| #33853 | 89 |