The problem of Weighted Sum Energy Efficiency (WSEE) Maximization of Device-to-Device (D2D) groups with underlaid Non-Orthogonal Multiple Access (NOMA) cellular network is investigated in this paper. In the novel network model, transmitters in each of the D2D groups will be able to communicate with multiple D2D receivers in the same spectral sub-band via NOMA protocol. Similarly, Base Station (BS) also communicates with multiple Cellular Users (CUs) via NOMA strategy. Power allocation for this hybrid network is presented in this paper. Optimization problem is formulated as WSEE Maximization of the D2D groups. This framework is suitable for energy-crunch devices, where the nodes can have different energy efficiency requirements. Further, to meet Quality of Service (QoS), rate constraints are imposed on all the receivers in the network. The optimization problem is challenging because of its non-convex sum-of-ratios form. So, it is first converted into an equivalent convex form. Subsequently, a successive convex approximation based algorithm is used to obtain optimal power distribution. The proposed power allocation algorithm is shown to be convergent and the simulation results closely match with the optimal values at all Signal-to-Noise Ratio (SNR) values.