We have studied the field and temperature dependence of the magnetization of single crystals of Sr3NiIrO6. These measurements evidence the presence of an easy axis of anisotropy and two anomalies in the magnetic susceptibility. Neutron powder diffraction realized on a polycrystalline sample reveals the emergence of magnetic reflections below 75 K with magnetic propagation vector k ~ (0, 0, 1), undetected in previous neutron studies [T.N. Nguyen and H.-C zur Loye, J. Solid State Chem., 117, 300 (1995)]. The nature of the magnetic ground state, and the presence of two anomalies common to this family of material, are discussed on the basis of the results obtained by neutron diffraction, magnetization measurements, and symmetry arguments.