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Let $\mathcal M$ be a weakly o-minimal non-valuational structure, and$\mathcal N$ its canonical o-minimal extension (by Wencel). We prove that everygroup $G$ definable in $\mathcal M$ is a subgroup of a group $K$ definable in$\mathcal N$, which is canonical in the sense that it is the smallest suchgroup. As an application, we obtain that $G^{00}= G\cap K^{00}$, and establishPillay's Conjecture in this setting: $G/G^{00}$, equipped with the logictopology, is a compact Lie group, and if $G$ has finitely satisfiable generics,then $\dim_{Lie}(G/G^{00})= \dim(G)$.

Groups definable in weakly o-minimal non-valuational structures