Structure, meaning a nonrandom arrangement of pores or pore domains, is present in many geologic porous media. We examined the effects of different nonrandom arrangements of the pore domains containing the largest pores on the percolation and flow properties of a simulated porous medium. Increasing the length of clusters (structural elements), or the fraction of the pore space occupied by them, decreases the percolation threshold (air entry value) and increases the permeability. Decreasing the internal homogeneity of clusters decreases the extent of their effects on percolation and permeability. Percolation threshold is not affected by the ratio between cluster length and network size as long as the cluster length is less than two thirds the network size. All cluster shapes display a similar relationship between percolation threshold and permeability, seen also in geologic porous media. The air entry value is a parameter that could potentially quantify both the degree of structure of a medium and its saturated permeability.