Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2250 conjugacy classes of subgroups.
The subgroup lattice has 290 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11739899 | C2 | semidirect |
| 4. #11739896 | C2 | semidirect |
| 10. C2×C4×C7×Q8 | C4 | semidirect |
| 108. C2×C4×Q8 | Dic7 | semidirect |
| 268. C7 | #34059 | 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 |
| #11741507 | 2 |
| #11739899 | 2 |
| #11739896 | 2 |
| #11739601 | 2 |
| #11739600 | 2 |
| #11739505 | 2 |
| C4×#6489 | 2 |
| #34059 | 7 |