One of the important indices defined for a set of vertices in a graph is group betweenness centrality. While in recent years a number of approximate algorithms have been proposed to estimate this index, there is no comprehensive and in-depth analysis and comparison of these algorithms in the literature. In this paper, we first present a generic algorithm that is used to express different approximate algorithms in terms of probability distributions. Using this generic algorithm, we show that interestingly existing methods have the same theoretical accuracy. Then, we present an extension of distance-based sampling to group betweenness centrality, which is based on a new notion of distance between a single vertex and a set of vertices. In the end, to empirically evaluate efficiency and accuracy of different algorithms, we perform experiments over several real-world networks. Our extensive experiments reveal that those approximate algorithms that are based on shortest path sampling are orders of magnitude faster than those algorithms that are based on pair sampling, while these two types of algorithms have almost comparable empirical accuracy.