Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1073 conjugacy classes of subgroups.
The subgroup lattice has 343 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #10589168 | C2 | direct (N × H) |
| 13. C2×C3×#208 | C4 | semidirect |
| 37. C3×#208 | C2×C4 | semidirect |
| 62. C2×#208 | Dic3 | semidirect |
| 131. #208 | C2×Dic3 | semidirect |
| 218. C2×C32 | #343 | semidirect |
| 278. C32 | C2×#343 | semidirect |
| 312. C2×C3 | #4554 | semidirect |
| 334. C3 | C2×#4554 | semidirect |
| 338. C2 | #10589168 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊(C3⋊Dic3) | 2 |
| C22×C3×#208 | 2 |
| #10589168 | 2 |
| C2×#4554 | 3 |