Genetic bistable systems are a large class of important biological systems. Bistability, the capacity to achieve two distinct stable steady states in response to a set of external stimuli, arises within biological systems ranging from the λ phage switch in bacteria to cellular signal transduction pathways in mammalian cells. On the other hand, the increasing experimental evidence in the form of bimodal population distribution has indicated that noise plays a very key role in the switching of bistable systems. However, the physiological mechanism underling noise-induced switching behaviors has not been well explored yet. In the previous work, it has been showed that noise can induce coherent switch for a single genetic Toggle switch system. Here the influence of several kinds of noises (including intracellular and extracellular noises) on synchronized switch was investigated for a multicell gene toggle switch network system. It has been found that multiplicative noises resulting from fluctuations of either synthesis or degradation rates and the additive noise within each cell (they altogether are called as intracellular noises) all can induce the synchronized switch, and that there exists an optimal noise intensity such that the synchronized switch is optimally achieved and the amplification factor has the maximal value. On the other hand, the extracellular noises arising from the stochastic fluctuation of the cellular environment, not only brings about the synchronized switch, but also enhances it by suppressing intracellular fluctuations when the intracellular noises are not enough to induce the synchronized switch. Finally, the influence of the diffusive rate of signal molecules affected by noise on the dynamics of the multicellular system was also investigated, showing that the larger the diffusive rate, the better the synchronized switch and the larger the amplification factor.