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 |
|---|---|---|
| 7. #11731088 | C2 | direct (N × H) |
| 19. C2×C4×Dic14 | C4 | semidirect |
| 64. C4×Dic14 | C2×C4 | semidirect |
| 280. C2×C7 | #2356 | semidirect |
| 322. C7 | C2×#2356 | semidirect |
| 341. C2 | #11731088 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×Dic14 | 2 |
| C2×C4×C7×C4⋊C4 | 2 |
| C2×#89750 | 2 |
| C2×#89701 | 2 |
| C2×#89708 | 2 |
| C2×C4×C4⋊Dic7 | 2 |
| #11731088 | 2 |
| C2×#89423 | 2 |
| C2×#89420 | 2 |
| C2×#2356 | 7 |