Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1026 conjugacy classes of subgroups.
The subgroup lattice has 524 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #11729580 | C2 | semidirect |
| 5. #11729578 | C2 | semidirect |
| 6. #11729376 | C2 | semidirect |
| 38. Q8⋊(C7⋊C8) | C22 | semidirect |
| 490. C7 | #17486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#533 | 2 |
| C2×#89697 | 2 |
| C2×#89696 | 2 |
| #11729580 | 2 |
| #11729578 | 2 |
| #11729376 | 2 |
| #17486 | 7 |