We find new exact solutions of the Einstein field equations for a perfect fluid metric conformal to a spacetime of type D in the Petrov classification scheme. We analyse the complete system of equations using Lie group analysis. While previous work was confined to conformal factors of the form U = U(t, x), we investigate the complete situation U = U(t, x, y, z) as well as an auxiliary integrability condition. New classes of solutions are generated via the symmetry generators. The resulting solutions are examined for physical plausibility. Expressions for the energy density and pressure are obtained explicitly and empirical results suggest that these dynamical quantities are positive as expected.