Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2122 conjugacy classes of subgroups.
The subgroup lattice has 360 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #82515 | C2 | semidirect |
| 4. #82209 | C2 | semidirect |
| 5. #82202 | C2 | semidirect |
| 6. #82049 | C2 | semidirect |
| 7. C2×#4924 | C2 | semidirect |
| 23. #5000 | C22 | semidirect |
| 24. #4997 | C22 | semidirect |
| 25. #4926 | C22 | semidirect |
| 26. #4925 | C22 | semidirect |
| 29. #4924 | C22 | semidirect |
| 30. C2×C4⋊(C3⋊C8) | C22 | semidirect |
| 353. C3 | #60125 | 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 |
| #84074 | 2 |
| #82515 | 2 |
| #82209 | 2 |
| #82202 | 2 |
| #82049 | 2 |
| C2×#4924 | 2 |
| #60125 | 3 |