How to find number of homomorphisms between z8 and s4?

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How to find number of homomorphisms between z8 and s4? I check by taking image of generator of z8 Say f:z8---->s4 O(f(1))/8 O(f(1))=1,2,4 S4 has 15 elements of order 2 and 6 elements of order 4 15+6+1(trivial)=22 Is this correct?