Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2810 conjugacy classes of subgroups.
The subgroup lattice has 298 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 | direct (N × H) |
| 4. C2×#4999 | C2 | semidirect |
| 5. C2×#4924 | C2 | semidirect |
| 6. C22×C4⋊(C3⋊C8) | C2 | semidirect |
| 21. #4999 | C22 | semidirect |
| 22. #4924 | C22 | semidirect |
| 27. C2×C4⋊(C3⋊C8) | C22 | semidirect |
| 175. C2×C3×C4 | #131 | semidirect |
| 239. C3×C4 | C2×#131 | semidirect |
| 256. C2×C4 | #948 | semidirect |
| 271. C2×C3 | #2906 | semidirect |
| 288. C4 | C2×#948 | semidirect |
| 291. C3 | C2×#2906 | semidirect |
| 293. C2 | #82512 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C4×#41 | 2 |
| C22×#948 | 2 |
| #82512 | 2 |
| C2×#4999 | 2 |
| C2×#4924 | 2 |
| C22×C4⋊(C3⋊C8) | 2 |
| C2×#2906 | 3 |