Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2250 conjugacy classes of subgroups.
The subgroup lattice has 294 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11739908 | C2 | semidirect |
| 4. #11739907 | C2 | semidirect |
| 10. C2×C4×C7×Q8 | C4 | semidirect |
| 109. C2×C4×Q8 | Dic7 | semidirect |
| 272. C7 | #34187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C7×Q8 | 2 |
| #11741507 | 2 |
| #11739908 | 2 |
| #11739907 | 2 |
| #11739600 | 2 |
| #11739589 | 2 |
| #11739507 | 2 |
| #11739505 | 2 |
| #34187 | 7 |