Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
4770 conjugacy classes of subgroups.
The subgroup lattice has 326 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#90510 | C2 | semidirect |
| 3. #11741557 | C2 | direct (N × H) |
| 4. C2×#90009 | C2 | semidirect |
| 5. C22×#6410 | C2 | semidirect |
| 16. #90510 | C22 | semidirect |
| 19. #90009 | C22 | semidirect |
| 21. C2×#6410 | C22 | semidirect |
| 268. C2×C7 | #2889 | semidirect |
| 302. C7 | C2×#2889 | semidirect |
| 323. C2 | #11741557 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×2−1+4 | 2 |
| C2×#90510 | 2 |
| #11741557 | 2 |
| C2×#90009 | 2 |
| C22×#6410 | 2 |
| C2×#2889 | 7 |