Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
942 conjugacy classes of subgroups.
The subgroup lattice has 506 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #11725492 | C2 | semidirect |
| 11. C7×#407 | C4 | semidirect |
| 14. C2×C7×C22⋊C8 | C4 | semidirect |
| 23. #89979 | C4 | semidirect |
| 26. C2×C22⋊(C7⋊C8) | C4 | semidirect |
| 59. C7×C22⋊C8 | C2×C4 | semidirect |
| 67. C22⋊(C7⋊C8) | C2×C4 | semidirect |
| 148. #407 | Dic7 | semidirect |
| 153. C2×C22⋊C8 | Dic7 | semidirect |
| 266. C22⋊C8 | C2×Dic7 | semidirect |
| 456. C7 | #8114 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#407 | 2 |
| C2×#89983 | 2 |
| C2×#89979 | 2 |
| #11725492 | 2 |
| #8114 | 7 |