Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
632 conjugacy classes of subgroups.
The subgroup lattice has 528 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C22×C4⋊Dic89 | C4 | semidirect |
| 8. C2×#15667919 | C4 | semidirect |
| 10. #19151322 | C4 | semidirect |
| 14. #342×C89 | C4 | semidirect |
| 267. C89 | #7250 | semidirect |
| 276. #342 | Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151322 | 2 |
| #26018497 | 2 |
| C2×#342×C89 | 2 |
| #7250 | 89 |