Groups of order 7.2^n

This article discusses the groups of order $$7 \cdot 2^n$$, where $$n$$ varies over nonnegative integers. Note that any such group has a 7-Sylow subgroup which is cyclic group:Z7, and a 2-Sylow subgroup, which is of order $$2^n$$. Further, because order has only two prime factors implies solvable, any such group is a solvable group.