Let Mn denote the connect sum of n copies of S2 × S1. Laudenbach showed that the mapping class group Mod(Mn) is an extension of the group Out(Fn) by (ℤ/2)n, where the latter group is the 'sphere twist' subgroup of Mod(Mn). In joint work with N. Broaddus and A. Putman, we have shown that in fact this extension splits. In this talk, we will describe the splitting and highlight some simplifications of Laudenbach's original proof that arise from our techniques.