Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2122 conjugacy classes of subgroups.
The subgroup lattice has 360 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11739960 | C2 | semidirect |
| 4. #11739654 | C2 | semidirect |
| 5. #11739647 | C2 | semidirect |
| 6. #11739494 | C2 | semidirect |
| 7. C2×#89696 | C2 | semidirect |
| 22. #89772 | C22 | semidirect |
| 23. #89769 | C22 | semidirect |
| 24. #89698 | C22 | semidirect |
| 25. #89697 | C22 | semidirect |
| 28. #89696 | C22 | semidirect |
| 29. C2×C4⋊(C7⋊C8) | C22 | semidirect |
| 336. C7 | #60125 | 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 |
| #11741519 | 2 |
| #11739960 | 2 |
| #11739654 | 2 |
| #11739647 | 2 |
| #11739494 | 2 |
| C2×#89696 | 2 |
| #60125 | 7 |