Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
2306 conjugacy classes of subgroups.
The subgroup lattice has 304 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #82520 | C2 | semidirect |
| 3. #41×C3⋊C8 | C2 | semidirect |
| 4. #82435 | C2 | semidirect |
| 5. #82301 | C2 | semidirect |
| 6. C2×#4925 | C2 | semidirect |
| 20. Q8×C3⋊C8 | C22 | semidirect |
| 21. D4×C3⋊C8 | C22 | semidirect |
| 24. #4925 | C22 | semidirect |
| 25. #4925 | C22 | semidirect |
| 26. C2×C4⋊(C3⋊C8) | C22 | semidirect |
| 27. C2×C4×C3⋊C8 | C22 | semidirect |
| 34. C2×C3×#41 | C8 | semidirect |
| 91. C3×#41 | C2×C8 | semidirect |
| 92. C3×#41 | C2×C8 | semidirect |
| 93. C2×C3×Q8 | C2×C8 | semidirect |
| 95. C2×C3×D4 | C2×C8 | semidirect |
| 99. C22×C3×C4 | C2×C8 | semidirect |
| 127. C2×#41 | C3⋊C8 | semidirect |
| 193. #41 | C2×C3⋊C8 | semidirect |
| 194. #41 | C2×C3⋊C8 | semidirect |
| 195. C2×Q8 | C2×C3⋊C8 | semidirect |
| 197. C2×D4 | C2×C3⋊C8 | semidirect |
| 201. C22×C4 | C2×C3⋊C8 | semidirect |
| 297. C3 | #60276 | 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 |
| #82520 | 2 |
| #41×C3⋊C8 | 2 |
| #82435 | 2 |
| #82301 | 2 |
| C2×#4925 | 2 |
| #60276 | 3 |