We determine the subfactors
N ⊂ R of the hyperfinite II1-factor R with finite index for which the C∗-tensor
category of the associated (N,N)-bimodules is equivalent to the C∗-tensor category
𝒰𝒢 of all unitary finite dimensional representations of a given finite group G. It
turns out that every subfactor of that kind is isomorphic to a subfactor
RG⊂ (R ⊗ L(ℂr))H, where RG is the fixed point algebra under an outer action α
of G, H is a subgroup of G, ψ : H→U(ℂr) is a unitary finite dimensional
projective representation of H satisfying a certain additional condition and
(R ⊗ L(ℂr))H is the fixed point algebra under the action α∣H ⊗Adψ of H on
R ⊗ L(ℂr).
