Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
474 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 79 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×#19151391 | C2 | semidirect |
| 2. #26018417 | C2 | semidirect |
| 3. #26018415 | C2 | semidirect |
| 9. #532×C89 | C4 | semidirect |
| 12. #493×C89 | C4 | semidirect |
| 14. #492×C89 | C4 | semidirect |
| 16. C4×M16×C89 | C4 | semidirect |
| 30. C4⋊Q8×C89 | C2×C4 | semidirect |
| 33. #127×C89 | C2×C4 | semidirect |
| 41. C4×C8×C89 | C2×C4 | semidirect |
| 42. C4×C8×C89 | C2×C4 | semidirect |
| 135. C89 | #13584 | semidirect |
| 137. #532 | Dic89 | semidirect |
| 140. #493 | Dic89 | semidirect |
| 142. #492 | Dic89 | semidirect |
| 145. C4×M16 | Dic89 | semidirect |
| 158. C4⋊Q8 | C2×Dic89 | semidirect |
| 161. #127 | C2×Dic89 | semidirect |
| 172. C4×C8 | C2×Dic89 | semidirect |
| 173. C4×C8 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151391 | 2 |
| #26018417 | 2 |
| #26018415 | 2 |
| C89×#3151 | 2 |
| #13584 | 89 |