Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
4462 conjugacy classes of subgroups.
The subgroup lattice has 296 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C4×C7⋊#95 | C2 | direct (N × H) |
| 9. C22×C42×C7 | C4 | semidirect |
| 13. C22×C4×Dic7 | C4 | semidirect |
| 15. C2×C7⋊#95 | C4 | direct (N × H) |
| 38. C2×C42×C7 | C2×C4 | semidirect |
| 42. C2×C4×Dic7 | C2×C4 | semidirect |
| 43. C7⋊#95 | C2×C4 | direct (N × H) |
| 62. C22×C4×C7 | C42 | semidirect |
| 81. C22×Dic7 | C42 | semidirect |
| 94. C22×C42 | Dic7 | semidirect |
| 121. C2×C4×C7 | #95 | semidirect |
| 123. C2×C4×C7 | C2×C42 | semidirect |
| 133. C2×Dic7 | C2×C42 | semidirect |
| 158. C2×C42 | C2×Dic7 | semidirect |
| 180. C4×C7 | C2×#95 | semidirect |
| 206. C22×C4 | C4×Dic7 | semidirect |
| 220. C2×C7 | C4×#95 | semidirect |
| 257. C2×C4 | C7⋊#95 | direct (N × H) |
| 259. C2×C4 | C2×C4×Dic7 | semidirect |
| 264. C7 | C2×C4×#95 | semidirect |
| 286. C4 | C2×C7⋊#95 | direct (N × H) |
| 287. C2 | C4×C7⋊#95 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C42×C7 | 2 |
| C23×C4×Dic7 | 2 |
| C22×C7⋊#95 | 2 |
| C4×C7⋊#95 | 2 |
| C2×C4×#95 | 7 |