The talk focuses on developing and analyzing efficient block preconditioners based on algebraic multigrid (AMG) for the large-scale sparse linear systems arising from the fully coupled and implicitly cell-centered finite volume discretization of multi-group radiation diffusion equations. The preconditioning techniques are the monolithic AMG method, lower and upper block triangular preconditioners, physical-variable based coarsening two-level algorithm and two types of block Schur complement preconditioners. The coupling strength and diagonal dominance are further explored to improve performance. We take advantage of representative one- and twenty-group linear systems from capsule implosion simulations to test the robustness, efficiency, strong and weak parallel scaling properties of the proposed methods.