Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
2810 conjugacy classes of subgroups.
The subgroup lattice has 298 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #11739957 | C2 | direct (N × H) |
| 4. C2×#89771 | C2 | semidirect |
| 5. C2×#89696 | C2 | semidirect |
| 6. C22×C4⋊(C7⋊C8) | C2 | semidirect |
| 20. #89771 | C22 | semidirect |
| 21. #89696 | C22 | semidirect |
| 26. C2×C4⋊(C7⋊C8) | C22 | semidirect |
| 140. C2×C4×C7 | #131 | semidirect |
| 202. C4×C7 | C2×#131 | semidirect |
| 243. C2×C7 | #2906 | semidirect |
| 261. C2×C4 | #6511 | semidirect |
| 275. C7 | C2×#2906 | semidirect |
| 289. C4 | C2×#6511 | semidirect |
| 293. C2 | #11739957 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C7×#41 | 2 |
| C22×#6511 | 2 |
| #11739957 | 2 |
| C2×#89771 | 2 |
| C2×#89696 | 2 |
| C22×C4⋊(C7⋊C8) | 2 |
| C2×#2906 | 7 |