Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2738 conjugacy classes of subgroups.
The subgroup lattice has 248 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #82512 | C2 | semidirect |
| 4. #82204 | C2 | semidirect |
| 5. C2×#4924 | C2 | semidirect |
| 18. #4999 | C22 | semidirect |
| 21. #4924 | C22 | semidirect |
| 22. C2×C4⋊(C3⋊C8) | C22 | semidirect |
| 199. C3×C4 | #568 | semidirect |
| 239. C4 | #5819 | semidirect |
| 242. C3 | #60099 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×#41 | 2 |
| C2×#5819 | 2 |
| #82512 | 2 |
| #82204 | 2 |
| C2×#4924 | 2 |
| #60099 | 3 |