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H\"older's theorem states that any group acting freely by circlehomeomorphisms is abelian, this is no longer true for interval exchangetransformations: we first give examples of free actions of non abelian groups.Then after noting that finitely generated groups acting freely by IET arevirtually abelian, we classify the free actions of groups containing a copy of$\mathbb Z^2$, showing that they are ``conjugate" to actions in some specificsubgroups $G_n$, namely $G_n \simeq ({\mathcal G}_2)^n \rtimes\mathcal S_n $where ${\mathcal G}_2$ is the group of circular rotations seen as exchanges of$2$ intervals and $\mathcal S_n$ is the group of permutations of $\{1,...,n\}$acting by permuting the copies of ${\mathcal G}_2$. We also study non freeactions of virtually abelian groups and we obtain the same conclusion for anysuch group that contains a conjugate to a product of restricted rotations withdisjoint supports and without periodic points. As a consequence, we provideexamples of non virtually nilpotent subgroups of IETs. In particular, we showthat the group generated by $f\in G_n$ periodic point free and $g\notin G_n$ isnot virtually nilpotent. Moreover, we exhibit examples of finitely generatednon virtually nilpotent subgroups of IETs, some of them are metabelian andothers are not virtually solvable.

Interval Exchange Transformations groups. Free actions and dynamics of virtually abelian groups