Atomic force microscopy (AFM) and grazing incidence x-ray diffraction (GIXD) have been used to study the structure of self-assembled monolayers of CF3(CF2)(n)(CH2)(2)SH (n=11, 7, and 5) on the Au(111) surface. Surprisingly, although the nearest-neighbor fluorinated alkane thiol distance is very close to the lattice constant of a commensurate p(2X2) structure, the close-packed rows of molecules are rotated similar to 30 degrees with respect to the underlying gold lattice. That packing is incommensurate or at most only close to the high-order commensurate c(7X7) structure. The relative orientation of the organic monolayer and the Au(111) substrate has been determined unambiguously both with GIXD, and by AFM, taking advantage of an earlier finding (Ref. 1) that AFM tips can reversibly displace the thiol molecules under high loads. In addition, we demonstrate that the two techniques provide complementary information on the order and the domain structures of these monolayers.