This paper explore some extropy properties of the lifetime of coherent systems with the assumption that the lifetime distribution of system components are independent and identically distributed. The presented results are obtained using the concept of system signature. To this aim, we first provide an expression for extropy of the lifetime of coherent systems. Then, stochastic extropy comparisons are discussed for coherent systems under the condition that both systems have the same characteristic structure. In cases where the number of system components is large or the system has a complex structure, it is difficult or time-consuming to obtain the exact extropy value of the system lifetime. Therefore, bounds are also obtained for extropy. In addition, a new criterion for selecting a preferred system based on relative extropy is proposed, which considers the lifetime of the desired system closest to the parallel system.