On finite groups of order \(2^ 3pq\) (Q801035)

This paper determines the finite groups G of order \(2^ 3pq\), where \(p<q\) are odd primes. There exist 1669 different types of such groups, which where determined according to the following cases for G: 1) G has a Sylow-tower; 2) G has no Sylow-tower but is solvable; 3) G is not solvable. The last case is settled by using a result of \textit{R. Brauer} and \textit{H.-F. Tuan} [Bull. Am. Math. Soc. 51, 756-766 (1945; Zbl 0061.037)], which determines the simple groups of order \(2^ mpq\).