The goal of N-x contingency selection is to pick a subset of critical cases to assess their potential to initiate a severe crippling of an electric power grid. Even for a moderate-sized system there can be an overwhelmingly large number of contingency cases that need to be studied. The number grows exponentially with x. This combinatorial explosion renders any exhaustive search strategy computationally infeasible, even for small to medium sized systems. We propose a novel method for N-x contingency selection for x > 1 using group betweenness centrality and show that computation can be relatively decoupled from the problem size, and thus making contingency analysis feasible for large systems with x > 1. Consequently, it may be that N-x (for x > 1) contingency selection can be effectively deployed despite the combinatorial explosion of the number of potential N-x contingencies.