Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
694 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 694 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26021946 | C2 | semidirect |
| 3. #26021926 | C2 | semidirect |
| 5. #26020357 | C2 | semidirect |
| 6. #26020353 | C2 | semidirect |
| 15. #19152151 | C4 | semidirect |
| 18. C2×#15667999 | C4 | semidirect |
| 19. #19152075 | C4 | semidirect |
| 20. #19152073 | C4 | semidirect |
| 268. C89 | #12721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26034147 | 2 |
| #26021946 | 2 |
| #26021926 | 2 |
| #26021902 | 2 |
| #26020357 | 2 |
| #26020353 | 2 |
| C89×#2122 | 2 |
| #12721 | 89 |