Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2550 conjugacy classes of subgroups.
The subgroup lattice has 348 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 | direct (N × H) |
| 11. C2×C4×C7×Q8 | C4 | semidirect |
| 48. C4×C7×Q8 | C2×C4 | semidirect |
| 124. C2×C4×Q8 | Dic7 | semidirect |
| 196. C4×Q8 | C2×Dic7 | semidirect |
| 280. C2×C7 | #2356 | semidirect |
| 322. C7 | C2×#2356 | semidirect |
| 341. C2 | #11739908 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C7×Q8 | 2 |
| C2×#90002 | 2 |
| #11739908 | 2 |
| C2×#89753 | 2 |
| C2×C4⋊C4×Dic7 | 2 |
| C2×#89709 | 2 |
| C2×#89708 | 2 |
| C2×C4×C4⋊Dic7 | 2 |
| C2×#89704 | 2 |
| C2×#2356 | 7 |