Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
500 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26023219 | C2 | semidirect |
| 5. #26018646 | C2 | semidirect |
| 6. #26018153 | C2 | semidirect |
| 7. C89×#1286 | C2 | semidirect |
| 12. #19151809 | C4 | semidirect |
| 13. #19151799 | C4 | semidirect |
| 204. #1286 | D89 | semidirect |
| 205. C89 | #9182 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029726 | 2 |
| #26023219 | 2 |
| #26018811 | 2 |
| #26018748 | 2 |
| #26018646 | 2 |
| #26018153 | 2 |
| C89×#1286 | 2 |
| #9182 | 89 |