The bicontinuous inverse cubic,phase.(V-2 phase) formed in. amphiphilic systems consists. of bilayer networks with a long-range order. We have investigated effects of oscillatory shear on the orientation of the V2 phase with space group la3d formed-in a-nonionic surfactant (C12E2)/water system by using simultaneous measurements of rheology/small-angle X-ray scattering, It is shown that grain refining occurs, by applying the large amplitude oscillatory shear (LAOS) with a strain amplitude (gamma(0)) of similar to 20, which gives-the ratio-of the loss modulus (G '') to the storage modulus (G') (G ''/G' = tan delta) of similar to 100. On the other hand, orientation of the cubic lattice occurs when the small amplitude (gamma(0) approximate to 0.0004) oscillatory shear (SAOS) in the linear regime is applied to the sample just after the LAOS. Interestingly, the orientation. is strongly enhanced by the "medium amplitude" (gamma(0) approximate to 0.05) oscillatory shear ("MAOS") after the SAOS. When the MAOS is applied before-applying the LAOS; orientation-to-a particular direction is riot observed, indicating that the grain refining process by the LAOS is necessary for the orientation during the MAOS. The results of additional experiments show that the shear sequence "LAOS-MAOS" is effective for the orientation of the cubic lattice. When the LAOS and MAOS are applied to the sample alternatively, grain refining and-orientation occur during the LAOS and MAOS, respectively, indicating reversibility of the orientation. It is:Shown that (i) the degree of the orientation is dependent on gamma(0) and the frequency (omega) of the MAOS and (ii) relatively-higher orientation can be-obtained for the combination of gamma(0) and omega, which gives tan delta = 2-3. The lattice constant does not change throughout all the shearing processes and is equal to that before shearing within the experimental errors, indicating that the shear melting does not occur. These results suggest a possibility to control the orientation of the cubic lattice only by changing the conditions of oscillatory shear without using the epitaxial transition from other anisotropic phases, such as the hexagonal and lamellar phases.