Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2942 conjugacy classes of subgroups.
The subgroup lattice has 512 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 6. #71567 | C2 | direct (N × H) |
| 19. C2×C3⋊#95 | C4 | semidirect |
| 71. C3⋊#95 | C2×C4 | semidirect |
| 447. C2×C3 | #1442 | semidirect |
| 498. C3 | C2×#1442 | semidirect |
| 499. C2 | #71567 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C4⋊C4 | 2 |
| C22×C3⋊#95 | 2 |
| #71567 | 2 |
| C2×#1442 | 3 |