Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2250 conjugacy classes of subgroups.
The subgroup lattice has 310 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11739908 | C2 | semidirect |
| 4. #11739905 | C2 | semidirect |
| 5. #11739899 | C2 | semidirect |
| 6. #11739895 | C2 | semidirect |
| 11. C2×C4×C7×Q8 | C4 | semidirect |
| 117. C2×C4×Q8 | Dic7 | semidirect |
| 287. C7 | #34192 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C7×Q8 | 2 |
| Q8×C22⋊Dic7 | 2 |
| #11739908 | 2 |
| #11739905 | 2 |
| #11739899 | 2 |
| #11739895 | 2 |
| #11739605 | 2 |
| #11739505 | 2 |
| #34192 | 7 |