Construct some dihedral groups of order 2n (i.e. symmetries of an n-gon, Dn in the text, DihedralGroup(n) in Sage). Maybe all of them for 3≤n≤100. For each dihedral group, construct a list of the orders of each of the normal subgroups (so use .normal\_subgroups()). You may need to wait ten or twenty seconds for this to finish -- be patient. Observe enough examples to hypothesize a pattern to your observations, check your hypothesis against each of your examples and then state your hypothesis.