Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
686 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26023008 | C2 | semidirect |
| 4. #26018786 | C2 | semidirect |
| 5. #26018161 | C2 | semidirect |
| 6. #26018105 | C2 | semidirect |
| 11. #19151754 | C4 | semidirect |
| 12. #19151749 | C4 | semidirect |
| 274. C89 | #9524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029512 | 2 |
| #26023008 | 2 |
| #26020170 | 2 |
| #26018786 | 2 |
| #26018161 | 2 |
| #26018105 | 2 |
| C89×#1789 | 2 |
| #9524 | 89 |