Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
3006 conjugacy classes of subgroups.
The subgroup lattice has 216 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C2×#89771 | C2 | direct (N × H) |
| 5. C22×C4⋊(C7⋊C8) | C2 | semidirect |
| 18. #89771 | C22 | direct (N × H) |
| 19. C2×C4⋊(C7⋊C8) | C22 | semidirect |
| 43. C4⋊(C7⋊C8) | C23 | semidirect |
| 136. C22×C7 | #424 | semidirect |
| 174. C2×C7 | C2×#424 | semidirect |
| 198. C7 | C22×#424 | semidirect |
| 201. C22 | #89771 | direct (N × H) |
| 212. C2 | C2×#89771 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×#117 | 2 |
| C23×#1136 | 2 |
| C24×C7⋊C8 | 2 |
| C2×#89771 | 2 |
| C22×C4⋊(C7⋊C8) | 2 |
| C22×#424 | 7 |