Neural architecture search (NAS) enables finding the best-performing architecture from a search space automatically. Most NAS methods exploit an over-parameterized network (i.e., a supernet) containing all possible architectures (i.e., subnets) in the search space. However, the subnets that share the same set of parameters are likely to have different characteristics, interfering with each other during training. To address this, few-shot NAS methods have been proposed that divide the space into a few subspaces and employ a separate supernet for each subspace to limit the extent of weight sharing. They achieve state-of-the-art performance, but the computational cost increases accordingly. We introduce in this paper a novel few-shot NAS method that exploits the number of nonlinear functions to split the search space. To be specific, our method divides the space such that each subspace consists of subnets with the same number of nonlinear functions. Our splitting criterion is efficient, since it does not require comparing gradients of a supernet to split the space. In addition, we have found that dividing the space allows us to reduce the channel dimensions required for each supernet, which enables training multiple supernets in an efficient manner. We also introduce a supernet-balanced sampling (SBS) technique, sampling several subnets at each training step, to train different supernets evenly within a limited number of training steps. Extensive experiments on standard NAS benchmarks demonstrate the effectiveness of our approach. We will make our code and models publicly available online.