This paper will consider the growth of the number of normal subgroups in a nonabelian group under the direct product operation. The groups considered in this paper are dihedral groups and semidirect products with a similar structure. Many proofs will rely on the use of a key property of normal subgroups, namely closure under conjugation, to predict this growth.
Radil, Whitney, "The Growth in Normal Subgroups Under Direct Products" (2013). Honors Theses, 1963-2015. 18.