Private Networks (also known as Non-Public Networks) bring significant benefits to Industry 4.0. These networks are typically deployed on-premises of the enterprises, and their isolation from the public (consumer) networks improves the crucial aspects of security and reliability. Despite the isolation, insider attacks can be mounted on these networks. This paper analyses such attacks using attack patterns from Common Attack Pattern Enumerations and Classifications (CAPEC) database. The analysis uses attack graphs, to combine individual domains, in the context of human, device, and network vulnerabilities. The attack graphs help identify paths, the cumulative impact on the system, and possible defense techniques, including security controls to mitigate the impact. Using three sample attack graphs in the context of standalone private 5G networks, this paper analyses possible security mechanisms and captures the difference among legacy enterprise networks (including Wi-Fi for limited mobility), public networks, and private networks.