Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
614 conjugacy classes of subgroups.
The subgroup lattice has 374 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#19151340 | C2 | semidirect |
| 4. #26018133 | C2 | semidirect |
| 192. C89 | #9122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#13083558 | 2 |
| #26020014 | 2 |
| C2×#19151340 | 2 |
| #26018133 | 2 |
| C89×#2851 | 2 |
| #9122 | 89 |