Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1978 conjugacy classes of subgroups.
The subgroup lattice has 260 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11739881 | C2 | direct (N × H) |
| 3. C2×#89796 | C2 | semidirect |
| 16. #89796 | C22 | semidirect |
| 208. C2×C7 | #2983 | semidirect |
| 238. C7 | C2×#2983 | semidirect |
| 255. C2 | #11739881 | 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 |
| #11739881 | 2 |
| C2×#89796 | 2 |
| C2×#89698 | 2 |
| C2×#89697 | 2 |
| C2×#2983 | 7 |