Finding Permutations with Exclusions
Generate all permutations of 1,...,6 (outer loop below), and all binary numbers of length 6 (inner loop below), then combine each permutation in the first set with each one from the second set:
for π in permutations(1,...,6):
    for x in 000000,...,111111:
        output C(π[1],x[1]),...,C(π[6],x[6])

where $C(n,0) = n$, $C(n,1) = 13 - n$.