Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2894 conjugacy classes of subgroups.
The subgroup lattice has 268 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. #11739600 | C2 | direct (N × H) |
| 6. C2×#89753 | C2 | semidirect |
| 10. C22×C7×C4⋊C4 | C4 | semidirect |
| 22. #89753 | C22 | semidirect |
| 39. C2×C7×C4⋊C4 | C2×C4 | semidirect |
| 92. C22×C4⋊C4 | Dic7 | semidirect |
| 150. C2×C4⋊C4 | C2×Dic7 | semidirect |
| 209. C2×C7 | #2313 | semidirect |
| 243. C7 | C2×#2313 | semidirect |
| 262. C2 | #11739600 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C7×C4⋊C4 | 2 |
| C2×#89983 | 2 |
| C2×#89984 | 2 |
| C2×C4×C22⋊Dic7 | 2 |
| #11739600 | 2 |
| C2×#89753 | 2 |
| C2×#2313 | 7 |