The crystal structures of the intercalation compounds FexTiS2 (x = 1/3, 1/4), which show a behavior characteristic of a cluster-glass phase at low temperature, were refined by means of Rietveld analysis of neutron powder-diffraction data. When x = 1/3 the space group is P $($) over bar$$ 31c and a ($) over bar root 3a x ($) over bar root 3a x 2c superlattice is formed. When x = 1/4, the space group becomes C2/m and a 2 ($) over bar root 3a x 2a x 2c superlattice is formed. For both concentrations, the occupancy at the Fe sites is less than 1.0.