  In the paper we characterize all interassociates of some non-inverse
semigroups and describe up to isomorphism all three-element (strong)
doppelsemigroups and their automorphism groups. We prove that there exist $75$
pairwise non-isomorphic three-element doppelsemigroups among which $41$
doppelsemigroups are commutative. Non-commutative doppelsemigroups are divided
into $17$ pairs of dual doppelsemigroups. Also up to isomorphism there are $65$
strong doppelsemigroups of order $3$, and all non-strong doppelsemigroups are
not commutative.
