Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1746 conjugacy classes of subgroups.
The subgroup lattice has 398 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #79987 | C2 | direct (N × H) |
| 84. C2×Dic12 | Q8 | semidirect |
| 195. Dic12 | C2×Q8 | semidirect |
| 373. C2×C3 | #3390 | semidirect |
| 392. C3 | C2×#3390 | semidirect |
| 393. C2 | #79987 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5567 | 2 |
| C2×C3×#446 | 2 |
| #79987 | 2 |
| C2×#4829 | 2 |
| C2×#4850 | 2 |
| C2×#4716 | 2 |
| C2×#4702 | 2 |
| C2×C4×Dic12 | 2 |
| C2×#4683 | 2 |
| C2×#3390 | 3 |