Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2350 conjugacy classes of subgroups.
The subgroup lattice has 402 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #71592 | C2 | direct (N × H) |
| 10. C2×C3×#117 | C4 | semidirect |
| 12. C22×C3×C4⋊C4 | C4 | semidirect |
| 14. C22×C3×C42 | C4 | semidirect |
| 18. C2×#926 | C4 | semidirect |
| 46. C2×C3×C4⋊C4 | C2×C4 | semidirect |
| 54. C2×C3×C42 | C2×C4 | semidirect |
| 61. #926 | C2×C4 | semidirect |
| 74. C2×#117 | Dic3 | semidirect |
| 77. C22×C4⋊C4 | Dic3 | semidirect |
| 81. C22×C42 | Dic3 | semidirect |
| 159. C2×C4⋊C4 | C2×Dic3 | semidirect |
| 173. C2×C42 | C2×Dic3 | semidirect |
| 359. C2×C3 | #1740 | semidirect |
| 391. C3 | C2×#1740 | semidirect |
| 398. C2 | #71592 | 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 |
| C22×#926 | 2 |
| #71592 | 2 |
| C2×#4526 | 2 |
| C2×#1740 | 3 |