Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2830 conjugacy classes of subgroups.
The subgroup lattice has 280 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #82204 | C2 | direct (N × H) |
| 4. C2×#4999 | C2 | semidirect |
| 5. C2×#4924 | C2 | semidirect |
| 20. #4999 | C22 | semidirect |
| 21. #4924 | C22 | semidirect |
| 22. C2×C4⋊(C3⋊C8) | C22 | semidirect |
| 57. C4⋊(C3⋊C8) | C23 | semidirect |
| 254. C2×C3 | #2905 | semidirect |
| 273. C3 | C2×#2905 | semidirect |
| 276. C2 | #82204 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#117 | 2 |
| C23×#208 | 2 |
| #82204 | 2 |
| C2×#4999 | 2 |
| C2×#4924 | 2 |
| C2×#2905 | 3 |