Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
925 conjugacy classes of subgroups.
The subgroup lattice has 318 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#5024 | C2 | semidirect |
| 3. C3×Q8×C3⋊C8 | C2 | semidirect |
| 7. Q8×#208 | C3 | direct (N × H) |
| 28. #5024 | C2×C3 | semidirect |
| 29. Q8×C3⋊C8 | C2×C3 | semidirect |
| 46. C3×#208 | Q8 | direct (N × H) |
| 85. C32×Q8 | M16 | semidirect |
| 97. C3×C3⋊C8 | C2×Q8 | semidirect |
| 147. #208 | C3×Q8 | direct (N × H) |
| 181. C3×Q8 | #208 | direct (N × H) |
| 182. C3×Q8 | C3×M16 | semidirect |
| 216. C3⋊C8 | C2×C3×Q8 | semidirect |
| 271. C32 | Q8×M16 | semidirect |
| 274. Q8 | C3×#208 | direct (N × H) |
| 311. C3 | Q8×#208 | direct (N × H) |
| 312. C3 | C3×Q8×M16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×C4×Q8 | 2 |
| C3×#5024 | 2 |
| C3×Q8×C3⋊C8 | 2 |
| C3×#4924 | 2 |
| C3×C4×#208 | 2 |
| C3×Q8×M16 | 3 |
| Q8×#208 | 3 |