Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
3390 conjugacy classes of subgroups.
The subgroup lattice has 384 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#5212 | C2 | semidirect |
| 4. #72127 | C2 | semidirect |
| 5. #71546 | C2 | semidirect |
| 11. C22×C3×C22⋊C4 | C4 | semidirect |
| 15. C22×C4⋊Dic3 | C22 | semidirect |
| 18. C2×C3⋊#95 | C22 | semidirect |
| 19. C2×C3⋊#95 | C22 | semidirect |
| 64. C22×C22⋊C4 | Dic3 | semidirect |
| 87. C24×C3 | C4⋊C4 | semidirect |
| 105. C22×C3×C4 | C22⋊C4 | semidirect |
| 220. C24 | C4⋊Dic3 | semidirect |
| 243. C22×C4 | #217 | semidirect |
| 373. C3 | #14338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C3×C22⋊C4 | 2 |
| C2×#5247 | 2 |
| C2×#5212 | 2 |
| #72127 | 2 |
| #71546 | 2 |
| #14338 | 3 |