Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
616 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 |
|---|---|---|
| 4. #11728507 | C2 | semidirect |
| 5. #11728505 | C2 | semidirect |
| 6. #11727605 | C2 | semidirect |
| 29. #89253 | C22 | semidirect |
| 30. #89252 | C22 | semidirect |
| 329. C7 | #17823 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2920 | 2 |
| #11739494 | 2 |
| #11728507 | 2 |
| #11728505 | 2 |
| #11727605 | 2 |
| #17823 | 7 |