Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2036 conjugacy classes of subgroups.
The subgroup lattice has 276 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×#4531 | C2 | semidirect |
| 10. C3×C4×#41 | C4 | semidirect |
| 13. Dic3×#41 | C4 | semidirect |
| 16. C2×#948 | C4 | semidirect |
| 39. C3×#117 | C2×C4 | semidirect |
| 43. C2×C3×C42 | C2×C4 | semidirect |
| 50. #926 | C2×C4 | semidirect |
| 53. C2×C4×Dic3 | C2×C4 | semidirect |
| 56. C2×#208 | C2×C4 | semidirect |
| 58. C22×C3⋊C8 | C2×C4 | semidirect |
| 71. C4×#41 | Dic3 | semidirect |
| 138. #117 | C2×Dic3 | semidirect |
| 145. C2×C42 | C2×Dic3 | semidirect |
| 269. C3 | #20338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3428 | 2 |
| #87260 | 2 |
| C2×#5819 | 2 |
| C2×#4531 | 2 |
| #20338 | 3 |