The neutrosophic set (NS) can be better to express the incomplete, indeterminate and inconsistent information, and Hamacher aggregation operators extended the Algebraic and Einstein aggregation operators and the generalized aggregation operators can generalize the arithmetic, geometric, and quadratic aggregation operators. In this paper, we combined Hamacher operations and generalized aggregation operators to NS, and proposed some new aggregation operators. Firstly, we presented some new operational laws for neutrosophic numbers (NNs) based on Hamacher operations and studied their properties. Then, we proposed the generalized neutrosophic number Hamacher weighted averaging (GNNHWA) operator, generalized neutrosophic number Hamacher ordered weighted averaging (GNNHOWA) operator, and generalized neutrosophic number Hamacher hybrid averaging (GNNHHA) operator, and explored some properties of these operators and analyzed some special cases of them. Furthermore, we gave a new method based on these operators for multiple attribute group decision making problems with neutrosophic numbers, and the operational steps were illustrated in detail. Finally, an application example is given to verify the proposed method and to demonstrate its effectiveness.