Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1702 conjugacy classes of subgroups.
The subgroup lattice has 348 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11740778 | C2 | semidirect |
| 3. #11740777 | C2 | semidirect |
| 4. #11740776 | C2 | semidirect |
| 5. Q8×#1136 | C2 | semidirect |
| 21. #89796 | C22 | semidirect |
| 22. #89796 | C22 | semidirect |
| 23. Q8×C7⋊C8 | C22 | semidirect |
| 324. C7 | #60249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#533 | 2 |
| #11740778 | 2 |
| #11740777 | 2 |
| #11740776 | 2 |
| Q8×#1136 | 2 |
| #11739654 | 2 |
| #11739494 | 2 |
| #60249 | 7 |