Abelian subgroups of maximum order need not be isomorphic

Statement
It is possible to have a group of prime power order $$P$$ with Abelian subgroups $$A, B$$ of maximum order such that $$A$$ is not isomorphic to $$B$$.

Example of the dihedral group
Let $$P$$ be the dihedral group of order eight, specifically:

$$P = \langle a,x \mid a^4 = x^2 = e, xax^{-1} = a^{-1} \rangle$$.

$$P$$ has three Abelian subgroups of maximum order (i.e., order four): the cyclic subgroup $$A$$ generated by $$a$$, and the following two Klein-four groups: the group $$B = \langle a^2,x \rangle$$, and the group $$C = \langle a^2, ax \rangle $$. $$A$$ is not isomorphic to either $$B$$ or $$C$$.