Classification of groups of order 16

Question

I just went through Dummit and Fottee's book of Abstract algebra; I couldn't found unfortunately there any non-abelian group of order 16 in the classification table of the groups of small orders - order 1 to 20. Can anybody tell me whats wrong with these groups of order 16?

Answer 1

There are many non-abelian groups of order 16. The simplest example is the group of symmetries of a regular octagon, $D_{16}$.

I believe that they are not listed since a complete classification of the non-abelian groups of order 16 requires some knowledge of semidirect products (which are introduced in the next two sections).