Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
516 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 99 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. #26020329 | C2 | semidirect |
| 4. #26018106 | C2 | semidirect |
| 5. C89×#2921 | C2 | semidirect |
| 9. #19151499 | C4 | semidirect |
| 10. #19151499 | C4 | semidirect |
| 13. #19151467 | C4 | semidirect |
| 14. #19151463 | C4 | semidirect |
| 189. #2921 | D89 | semidirect |
| 194. C89 | #9446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26024710 | 2 |
| #26020329 | 2 |
| #26018782 | 2 |
| #26018106 | 2 |
| C89×#2921 | 2 |
| #9446 | 89 |