Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
1702 conjugacy classes of subgroups.
The subgroup lattice has 348 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #83333 | C2 | semidirect |
| 3. #83332 | C2 | semidirect |
| 4. #83331 | C2 | semidirect |
| 5. Q8×#208 | C2 | semidirect |
| 22. #5024 | C22 | semidirect |
| 23. #5024 | C22 | semidirect |
| 24. Q8×C3⋊C8 | C22 | semidirect |
| 341. C3 | #60249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#533 | 2 |
| #83333 | 2 |
| #83332 | 2 |
| #83331 | 2 |
| Q8×#208 | 2 |
| #82209 | 2 |
| #82049 | 2 |
| #60249 | 3 |