Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
460 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26020245 | C2 | semidirect |
| 5. #26018646 | C2 | semidirect |
| 6. #26018149 | C2 | semidirect |
| 7. C89×#1570 | C2 | semidirect |
| 176. #1570 | D89 | semidirect |
| 181. C89 | #10443 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151799 | 2 |
| #26020245 | 2 |
| #26018921 | 2 |
| #26018919 | 2 |
| #26018646 | 2 |
| #26018149 | 2 |
| C89×#1570 | 2 |
| #10443 | 89 |