Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2022 conjugacy classes of subgroups.
The subgroup lattice has 272 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11739882 | C2 | direct (N × H) |
| 3. C2×#89796 | C2 | semidirect |
| 4. C2×Q8×C7⋊C8 | C2 | semidirect |
| 18. #89796 | C22 | semidirect |
| 19. Q8×C7⋊C8 | C22 | semidirect |
| 220. C2×C7 | #2984 | semidirect |
| 250. C7 | C2×#2984 | semidirect |
| 267. C2 | #11739882 | 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 |
| #11739882 | 2 |
| C2×#89796 | 2 |
| C2×Q8×C7⋊C8 | 2 |
| C2×#89698 | 2 |
| C2×#89697 | 2 |
| C2×#2984 | 7 |