We report on 13C NMR measurements above and below the clearing temperature of the liquid crystal 4-n-hexyloxyphenyl 4-methoxybenzoate constrained to an oriented, low concentration polymer network. The network is obtained by UV-irradiation of the reactive monomer 1,4-di-[4-(6-acryloyloxyhexyloxy)benzoyloxy]-2-methylbenzene which is in admixture with the liquid crystal. The characterization of orientational order of the mixtures before UV-radiation, and hence before polymerization, reveals the high order of the components at the polymerization temperature. The chosen geometry explains the LC director orientation only by the aligned network. Above the nematic-isotropic transition a strong pretransitional order is detected. Fast molecular translational diffusion averages the order over dimensions smaller than 1 mum. The Landau-de Gennes theory predicts a relation between pretransitional order and the lateral dimension of the LC regions. The experimental data are successfully explained by pore diameters of 35 and 98 nm for concentrations of 20 and 8 mol% of monomer, respectively. The results support the model of nearly cylindrical shaped liquid crystal domains surrounded by thin walls of crosslinked network.