Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
474 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 59 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. #353×D89 | C2 | semidirect |
| 3. #26018416 | C2 | semidirect |
| 4. #26018415 | C2 | semidirect |
| 5. C89×#1408 | C2 | semidirect |
| 7. #19152146 | C4 | semidirect |
| 10. #19151974 | C4 | semidirect |
| 11. #19151971 | C4 | semidirect |
| 14. C4×#13083557 | C4 | semidirect |
| 28. #15668012 | C2×C4 | semidirect |
| 40. C4×#10623494 | C2×C4 | semidirect |
| 42. #127×C89 | C2×C4 | semidirect |
| 45. C4×C8×C89 | C2×C4 | semidirect |
| 141. #1408 | D89 | semidirect |
| 142. C89 | #13584 | semidirect |
| 170. #127 | C4×D89 | semidirect |
| 182. C4×C8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26030703 | 2 |
| #353×D89 | 2 |
| #26018416 | 2 |
| #26018415 | 2 |
| C89×#1408 | 2 |
| #13584 | 89 |