The folklore conjecture that almost all finite groups are 2-groups

Let a finite group be a group with finitely many elements, and call it a 2-group when its order is a power of $2$. Folklore conjecture. Almost all groups are $2$-groups. This conjecture is presented as a folklore claim that would nearly complete the classification of finite wreath products with surjective strategies; its precise meaning and current status are not specified in the source.