Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2586 conjugacy classes of subgroups.
The subgroup lattice has 240 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11741234 | C2 | direct (N × H) |
| 4. C2×#89897 | C2 | semidirect |
| 5. C22×#6393 | C2 | semidirect |
| 16. #89897 | C22 | semidirect |
| 19. C2×#6393 | C22 | semidirect |
| 195. C2×C7 | #2916 | semidirect |
| 220. C7 | C2×#2916 | semidirect |
| 237. C2 | #11741234 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×#131 | 2 |
| C2×#90510 | 2 |
| #11741234 | 2 |
| C2×#89897 | 2 |
| C22×#6393 | 2 |
| C2×#2916 | 7 |