Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
826 conjugacy classes of subgroups.
The subgroup lattice has 498 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #26018376 | C2 | semidirect |
| 6. C2×#15667971 | C4 | semidirect |
| 7. C22×C4⋊Dic89 | C4 | semidirect |
| 9. #19151572 | C4 | semidirect |
| 12. #19151505 | C4 | semidirect |
| 21. #410×C89 | C4 | semidirect |
| 42. #15667927 | C2×C4 | semidirect |
| 66. #99×C89 | C2×C4 | semidirect |
| 253. C89 | #12583 | semidirect |
| 262. #410 | Dic89 | semidirect |
| 313. #99 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151572 | 2 |
| #26022844 | 2 |
| #26018376 | 2 |
| C2×#410×C89 | 2 |
| #12583 | 89 |