Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
3006 conjugacy classes of subgroups.
The subgroup lattice has 270 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11739905 | C2 | semidirect |
| 4. #11739778 | C2 | semidirect |
| 5. #11739678 | C2 | semidirect |
| 6. #11739507 | C2 | semidirect |
| 7. C2×#89708 | C2 | semidirect |
| 9. C4×C7×#41 | C4 | semidirect |
| 38. C4×C7×Q8 | C2×C4 | semidirect |
| 39. C4×C7×D4 | C2×C4 | semidirect |
| 40. C7×#117 | C2×C4 | semidirect |
| 43. C2×C42×C7 | C2×C4 | semidirect |
| 68. C7×#41 | C4⋊C4 | semidirect |
| 101. C4×#41 | Dic7 | semidirect |
| 153. C4×Q8 | C2×Dic7 | semidirect |
| 155. C4×D4 | C2×Dic7 | semidirect |
| 157. #117 | C2×Dic7 | semidirect |
| 167. C2×C42 | C2×Dic7 | semidirect |
| 189. #41 | C4⋊Dic7 | semidirect |
| 249. C7 | #34184 | 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 |
| C2×#90518 | 2 |
| #11739905 | 2 |
| #11739778 | 2 |
| #11739678 | 2 |
| #11739507 | 2 |
| C2×#89708 | 2 |
| #34184 | 7 |