Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
4334 conjugacy classes of subgroups.
The subgroup lattice has 346 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×#4526 | C2 | direct (N × H) |
| 6. C24×C3×C4 | C4 | semidirect |
| 10. C22×C3×C22⋊C4 | C4 | semidirect |
| 14. C22×#217 | C4 | semidirect |
| 16. #4526 | C22 | direct (N × H) |
| 32. C23×C3×C4 | C2×C4 | semidirect |
| 40. C2×C3×C22⋊C4 | C2×C4 | semidirect |
| 45. C2×#217 | C2×C4 | semidirect |
| 49. C24×C4 | Dic3 | semidirect |
| 56. C22×C22⋊C4 | Dic3 | semidirect |
| 92. C22×C3×C4 | C22×C4 | semidirect |
| 101. #217 | C22×C4 | semidirect |
| 117. C23×C4 | C2×Dic3 | semidirect |
| 127. C2×C22⋊C4 | C2×Dic3 | semidirect |
| 213. C22×C4 | C22×Dic3 | semidirect |
| 237. C22×C3 | #342 | semidirect |
| 302. C2×C3 | C2×#342 | semidirect |
| 323. C22 | #4526 | direct (N × H) |
| 335. C3 | C22×#342 | semidirect |
| 342. C2 | C2×#4526 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C22⋊C4 | 2 |
| C23×#217 | 2 |
| C2×#4526 | 2 |
| C22×#342 | 3 |