Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2830 conjugacy classes of subgroups.
The subgroup lattice has 280 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11739649 | C2 | direct (N × H) |
| 4. C2×#89771 | C2 | semidirect |
| 5. C2×#89696 | C2 | semidirect |
| 19. #89771 | C22 | semidirect |
| 20. #89696 | C22 | semidirect |
| 21. C2×C4⋊(C7⋊C8) | C22 | semidirect |
| 52. C4⋊(C7⋊C8) | C23 | semidirect |
| 224. C2×C7 | #2905 | semidirect |
| 257. C7 | C2×#2905 | semidirect |
| 276. C2 | #11739649 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×#117 | 2 |
| C23×#1136 | 2 |
| #11739649 | 2 |
| C2×#89771 | 2 |
| C2×#89696 | 2 |
| C2×#2905 | 7 |