Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2738 conjugacy classes of subgroups.
The subgroup lattice has 248 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11739957 | C2 | semidirect |
| 4. #11739649 | C2 | semidirect |
| 5. C2×#89696 | C2 | semidirect |
| 17. #89771 | C22 | semidirect |
| 20. #89696 | C22 | semidirect |
| 21. C2×C4⋊(C7⋊C8) | C22 | semidirect |
| 167. C4×C7 | #568 | semidirect |
| 229. C7 | #60099 | semidirect |
| 240. C4 | #90510 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×#41 | 2 |
| C2×#90510 | 2 |
| #11739957 | 2 |
| #11739649 | 2 |
| C2×#89696 | 2 |
| #60099 | 7 |