The low-lying candidates of Ge65, Ge70 and Ge75 are extensively investigated through combining the tight-binding potential of germanium with two kinds of global minima search strategies: compressing liquid and genetic algorithm. Then, we perform accurate ab initio calculations to optimize the atomic structures of these low-lying candidates and identify the ground state structures. Our calculations predict that there exist two kinds of stable isomers characterizing the sphere- and ellipsoid-like structural features for each sized cluster, and the two kinds of isomers are energetically competitive. This is consistent with the observation for the large sized clusters Gen (65 ≤ n ≤ 80) in experiment. Meanwhile, we also briefly analyze the electronic properties of these three kinds of clusters.