We analyze the growth rates of perturbations of the generic dust-filled Bianchi type-I cosmology (which exhibits anisotropy but not rotation). Anisotropy induces coupling between gravitational wave and density modes and can enhance the power-law rate of growth of the density perturbations. A maximum growth rate for pregalaxy perturbations is ${t}^{\frac{8}{3}}$ (where $t$ is cosmic time), so that no conclusive solution to the galaxy formation problem is found. The detailed structure of the flow of energy between gravitational wave and density modes and of the growth of rotational modes (decoupled from other perturbations) is presented. We also give a detailed discussion of the gauge-invariance properties of these perturbations.