Given two positive integers n≥3 and t≤n, the permutations σ,π∈Sym(n) are t-setwise intersecting if they agree (setwise) on a t-subset of {1,2,…,n}. A family F⊂Sym(n) is t-setwise intersecting if any two permutations of F are t-setwise intersecting. Ellis (2012) 6 conjectured that if t≤n and F⊂Sym(n) is a t-setwise intersecting family, then |F|≤t!(n−t)! and equality holds only if F is a coset of a setwise stabilizer of a t-subset of {1,2,…,n}. In this paper, we prove that if n≥11 and F⊂Sym(n) is 3-setwise intersecting, then |F|≤6(n−3)!. Moreover, we prove that the characteristic vector of a 3-setwise intersecting family of maximum size lies in the sum of the eigenspaces induced by the permutation module of Sym(n) acting on the 3-subsets of {1,2,…,n}.