Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2110 conjugacy classes of subgroups.
The subgroup lattice has 330 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C3⋊#338 | C2 | direct (N × H) |
| 18. C3⋊#338 | C22 | direct (N × H) |
| 243. C22×C3 | #338 | semidirect |
| 300. C2×C3 | C2×#338 | semidirect |
| 310. C22 | C3⋊#338 | direct (N × H) |
| 322. C3 | C22×#338 | semidirect |
| 327. C2 | C2×C3⋊#338 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×M16 | 2 |
| C23×#208 | 2 |
| C2×C3⋊#338 | 2 |
| C22×#338 | 3 |