To clarify the effects of α-cluster breaking on 3α cluster structures in12C, we investigate12C using a hybrid model that combines the Brink-Bloch cluster model with the p3/2 subshell closure wave function. We have found that α-cluster breaking significantly changes the cluster structures of 0+ states through orthogonality to lower states. As a result of the structure changes of 0+ states, the band assignment for the state is changed. The state is likely to be the band-head of the state instead of the state because the present calculation reproduces experimental data of the low-lying states well with α-cluster breaking. We have found that this band can be considered a linear chain-like band from the analysis of the intrinsic structures.