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It is well-known that the quantum double $D(N\subset M)$ of a finite depthsubfactor $N\subset M$, or equivalently the Drinfeld center of the even partfusion category, is a unitary modular tensor category. Thus should arise inconformal field theory. We show that for every subfactor $N\subset M$ withindex $[M:N]<4$ the quantum double $D(N\subset M)$ is realized as therepresentation category of a completely rational conformal net. In particular,the quantum double of $E_6$ can be realized as a $\mathbb Z_2$-simple currentextension of $\mathrm{SU}(2)_{10}\times \mathrm{Spin}(11)_1$ and thus is notexotic in any sense. As a byproduct we obtain a vertex operator algebra forevery such subfactor.  We obtain the result by showing that if a subfactor $N\subset M $ arises from$\alpha$-induction of completely rational nets $\mathcal A\subset \mathcal B$and there is a net $\tilde{\mathcal A}$ with the opposite braiding, then thequantum $D(N\subset M)$ is realized by completely rational net. We constructcompletely rational nets with the opposite braiding of $\mathrm{SU}(2)_k$ anduse the well-known fact that all subfactors with index $[M:N]<4$ arise by$\alpha$-induction from $\mathrm{SU}(2)_k$.

A Remark on CFT Realization of Quantum Doubles of Subfactors. Case Index < 4