A dedicated subnetwork (DSN) refers to a subset of lanes, with associated loads, in a shipper's transportation network, for which resources—trucks, drivers, and other equipment—are exclusively assigned to accomplish shipping requirements. The resources assigned to a DSN are not shared with the rest of the shipper's network. Thus, a DSN is an autonomously operated subnetwork and, hence, can be subcontracted. We address a novel problem of extracting a DSN for outsourcing to one or more subcontractors, with the objective of maximizing the shipper's savings. In their pure form, the defining conditions of a DSN are often too restrictive to enable the extraction of a sizable subnetwork. We consider two notions—deadheading and lane-sharing—that aid in improving the size of the DSN. We show that all the optimization problems involved are both strongly NP-hard and APX-hard, and demonstrate several polynomially solvable special cases arising from topological properties of the network and parametric relationships. Next, we develop a network-flow-based heuristic that provides near-optimal solutions to practical instances in reasonable time. Finally, using a test bed based on data obtained from a national 3PL company, we demonstrate the substantial monetary impact of subcontracting a DSN and offer useful managerial insights.