semimagic squares: 1, 0, 9, ...

[Eric W. Weisstein]

There are nine *semimagic* (cf. A006052) squares of order 3 modulo
rotation/reflection:

{{{1, 5, 9}, {6, 7, 2}, {8, 3, 4}},
{{1, 5, 9}, {8, 3, 4}, {6, 7, 2}},
{{1, 6, 8}, {9, 2, 4}, {5, 7, 3}},
{{1, 8, 6}, {9, 4, 2}, {5, 3, 7}},
{{2, 4, 9}, {6, 8, 1}, {7, 3, 5}},
{{2, 6, 7}, {9, 1, 5}, {4, 8, 3}},
{{2, 7, 6}, {9, 5, 1}, {4, 3, 8}},
{{3, 4, 8}, {5, 9, 1}, {7, 2, 6}},
{{3, 7, 5}, {8, 6, 1}, {4, 2, 9}}}

How many are there for higher orders?  Any takers?

Cheers,
-E