It has been shown that CeSix exhibits a variety of interesting physical properties, however the magnetic ground state was unclear due to the possible coexistence of multiple magnetic phases. In this study, the physical properties of CeSix with 1.57≪x≤2.0 have been investigated to clarify the magnetic ordering ground states throughout the series. For Si concentrations greater than 1.80, samples are paramagnetic. Ferromagnetic ordering first appears when Si concentration is decreased to 1.80. For Si concentrations ranging from 1.73 to 1.80, TC=13.8 K. As Si concentration is further decreased below 1.73, TC steps down to 12 K, remaining constant down to the lowest concentration studied, x=1.57. Interestingly, the latter change in magnetic ground state is accompanied by a structural distortion from the ThSi2-type tetragonal structure to the GdSi2-type orthorhombic phase. In the magnetic regime, zero-field-cooled and field-cooled magnetization data are irreversible, indicating a strong domain-wall pinning effect. Values of TC are corroborated by specific-heat and resistivity measurements.