Network intrusion poses a severe threat to the Internet of Things (IoT). Thus, it is essential to study information security protection technology in IoT. Learning sophisticated feature interactions is critical in improving detection accuracy for network intrusion. Despite significant progress, existing methods seem to have a strong bias towards single low- or high-order feature interaction. Moreover, they always extract all possible low-order interactions indiscriminately, introducing too much noise. To address the above problems, we propose a low-order correlation and high-order interaction (LCHI) integrated feature extraction model. First, we selectively extract the beneficial low-order correlation between the same-type features by the multivariate correlation analysis (MCA) model and attention mechanism. Second, we extract the complicated high-order feature interaction by the deep neural network (DNN) model. Finally, we emphasize both the low- and high-order feature interactions and incorporate them. Our LCHI model seamlessly combines the linearity of MCA in modeling lower-order feature correlation and the nonlinearity of DNN in modeling higher-order feature interaction. Conceptually, our LCHI is more expressive than the previous models. We carry on a series of experiments on the public wireless and wired network intrusion detection datasets. The experimental results show that LCHI improves 1.06%, 2.46%, 3.74%, 0.25%, 1.17%, and 0.64% on the AWID, NSL-KDD, UNSW-NB15, CICIDS 2017, CICIDS 2018, and DAPT 2020 datasets, respectively.