Using the notion of semidirect products and the cyclic extensions to find groups of order thirty-two.

[1] G.A. Miller, H.F. Blichfeldt and L.E. Dickson. Theory and applications of finite groups, Dover Publications(
New York,1961)
[2] Rotman, Joseph J. An introduction to the theory of groups, Springer-Verlag(New York, 1995)
[3] A.D. Thomas and G.V. Wood. Group Tables, Mathematics Series 2, Shiva Publishing Limited, Kent,UK,1980.
[4] David S. Dummit and Richard M. Foote. Abstract algebra, Prentice Hall Inc., Englewood Cliffs, NJ, 2nd edition, 1999.
[5] Gorenstein Daniel. Finite groups, Harper and Row,Publishers (New York, 1967)
[6] Marcel Wild. The groups of order sixteen made easy, American Mathematical Monthly 112 (2005) 20–31.
[7] Hans Ulrich Besche, Bettina Eick, E. A. O’Brien. A Millennium Project:Constructing Small Groups, International
Journal of Algebra and Computation, Vol. 12, No. 5 (2002) 623–644.
[8] R. Levavasseur. Sur les groupes d′op´erations I, C. R. Acad. Sci. Paris Vie Acad ´ emique122 (1896), 180–182.
[9] G. A. Miller. The regular substitution groups whose orders are less than 48, Quart.J. Math. 28 (1896), 232–
284.
[10] G. A. Miller. General theorems applying to all the groups of order 32, Proc. Nat. Acad. Sci. USA 22 (1936),
112–115.
[11] G. Bagnera. Sopra i gruppi astratti di grado 32, Ann. Mat. Pura Appl. 2(3)(1899), 263–275.
[12] M. Sophie. A note on the groups of order thirty-two, Illinois J. Math. 6 (1962), 630–633.
[13] GAP—Groups, Algorithms, Programming, version4.4.10, http://www.gap-system.org