Speech enhancement in multichannel settings has been realized by utilizing the spatial information embedded in multiple microphone signals. Moreover, deep neural networks (DNNs) have been recently advanced in this field; however, studies on the efficient multichannel network structure fully exploiting spatial information and inter-channel relationships is still in its early stages. In this study, we propose an end-to-end time-domain speech enhancement network that can facilitate the use of inter-channel relationships at individual layers of a DNN. The proposed technique is based on a fully convolutional time-domain audio separation network (Conv-TasNet), originally developed for speech separation tasks. We extend Conv-TasNet into several forms that can handle multichannel input signals and learn inter-channel relationships. To this end, we modify the encoder-mask-decoder structures of the network to be compatible with 3-D tensors defined over spatial channels, features, and time dimensions. In particular, we conduct extensive parameter analyses on the convolution structure and propose independent assignment of the depthwise and 1$\times$1 convolution layers to the feature and spatial dimensions, respectively. We demonstrate that the enriched inter-channel information from the proposed network plays a significant role in suppressing noisy signals impinging from various directions. The proposed inter-channel Conv-TasNet outperforms the state-of-the-art multichannel variants of neural networks, even with one-tenth of their parameter size. The performance of the proposed model is evaluated using the CHiME-3 dataset, which exhibits a remarkable improvement in SDR, PESQ, and STOI.