Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
474 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 2. C2×#19151391 | C2 | semidirect |
| 3. #26018416 | C2 | semidirect |
| 4. #26018414 | C2 | semidirect |
| 5. C2×#353×C89 | C2 | semidirect |
| 8. #19152148 | C4 | semidirect |
| 11. #19151974 | C4 | semidirect |
| 13. #19151970 | C4 | semidirect |
| 16. C4×#13083558 | C4 | semidirect |
| 37. #15668012 | C2×C4 | semidirect |
| 38. #15668009 | C2×C4 | semidirect |
| 46. C4×#10623494 | C2×C4 | semidirect |
| 47. C4×#10623494 | C2×C4 | semidirect |
| 193. C2×#353 | D89 | semidirect |
| 196. C89 | #13584 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030702 | 2 |
| C2×#19151391 | 2 |
| #26018416 | 2 |
| #26018414 | 2 |
| C2×#353×C89 | 2 |
| #13584 | 89 |