Palindromic Prime Factors
05AB1E, 7 bytes

Òœ.ΔJÂQ


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Explanation:

Ò            # prime factorization of the input
 œ           # permutations
  .Δ         # find the first one such that
    J        # concatenated
     ÂQ      # is a palindrome


(.Δ conveniently defaults to -1, so no extra work needed)