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In this article, I study the shear thickening of suspensions of frictional dimers by the mean of numerical simulations. I report the evolution of the main parameters of shear thickening, such as the jamming volume fractions in the unthickened and thickened branches of the flow curves, as a function of the aspect ratio of the dimers. The explored aspect ratios range from $1$ (spheres) to $2$ (dimers made of two kissing spheres). I find a rheology qualitatively similar than the one for suspensions of spheres, except for the first normal stress difference $N_1$, which I systematically find negative for small asphericities. I also investigate the orientational order of the particles under flow. Overall, I find that dense suspensions of dimeric particles share many features with dry granular systems of elongated particles under shear, especially for the frictional state at large applied stresses. For the frictionless state at small stresses, I find that suspensions jam at lower volume fraction than dry systems, and that this difference increases with increasing aspect ratio. Moreover, in this state I find a thus far unobserved alignment of the dimers along the vorticity direction, as opposed to the commonly observed alignment with a direction close to the flow direction.