Based on a large database of local minima obtained with the polarizable AMOEBA potential, the generalized energy-based fragmentation (GEBF) approach is applied to locate low-lying structures of water clusters (H2O)(n) in the range n = 20-30, at the B3LYP and MP2 levels. Our results show that the relative stabilities of isomers predicted by the AMOEBA empirical potential differ noticeably from those predicted by GEBF-B3LYP/6-311++G(d,p) and GEBF-MP2/6-311++G(3df,2p) calculations. From GEBF-B3LYP energies with zero-point vibrational energy corrections, one can see that for water clusters in the range n = 20-30 the transition from one-centered to two-centered cage structure occurs at n = 26. With increasing cluster size, the number of H-bonds per water molecule in the lowest-energy structures shows a gradually increasing trend, and the proportion of four-coordinated water molecules gradually increases, as expected for large water clusters. Based on GEBF-MP2/6-311++G(3df,2p) energies (instead of GEBF-B3LYP/6-311++G(d,p) energies), different lowest-energy structures can be found for six cluster sizes in the range n = 20-30, suggesting the significance of the dispersion interaction in determining the relative energies of low-lying water clusters.