Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2350 conjugacy classes of subgroups.
The subgroup lattice has 594 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #71593 | C2 | direct (N × H) |
| 10. C2×C3×#117 | C4 | semidirect |
| 25. C2×#926 | C4 | semidirect |
| 26. C2×#926 | C4 | semidirect |
| 30. C22×C4⋊Dic3 | C4 | semidirect |
| 32. C22×C4×Dic3 | C4 | semidirect |
| 59. C3×#117 | C2×C4 | semidirect |
| 88. #926 | C2×C4 | semidirect |
| 94. C2×C4⋊Dic3 | C2×C4 | semidirect |
| 100. C2×C4×Dic3 | C2×C4 | semidirect |
| 116. C2×#117 | Dic3 | semidirect |
| 237. #117 | C2×Dic3 | semidirect |
| 536. C2×C3 | #1740 | semidirect |
| 580. C3 | C2×#1740 | semidirect |
| 590. C2 | #71593 | 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 |
| #71593 | 2 |
| C2×#4527 | 2 |
| C2×#1740 | 3 |