Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1124 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1124 conjugacy classes of subgroups — too many to draw. Only its 195 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. C23×Dic356 | C2 | semidirect |
| 2. C2×#19152041 | C2 | semidirect |
| 4. #26022188 | C2 | semidirect |
| 5. #26022171 | C2 | semidirect |
| 6. #26021973 | C2 | semidirect |
| 7. C89×#2112 | C2 | semidirect |
| 17. C2×Dic712 | C22 | semidirect |
| 18. C2×#15667957 | C22 | semidirect |
| 24. #19151403 | C22 | semidirect |
| 43. C2×Dic356 | D4 | semidirect |
| 153. C22×C89 | #510 | semidirect |
| 176. #2112 | D89 | semidirect |
| 177. C89 | #33518 | semidirect |
| 325. C22 | #19152041 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic356 | 2 |
| C2×#19152041 | 2 |
| #26029833 | 2 |
| #26022188 | 2 |
| #26022171 | 2 |
| #26021973 | 2 |
| C89×#2112 | 2 |
| #33518 | 89 |