The magic square legend

According to a legend, there was at one time in ancient China a huge flood. While the great king Yu was trying to channel the water out to sea, a turtle emerged from it with a curious pattern on its shell (see the image below): a magic square, i.e. a \(nxn\) square grid filled with distinct positive integers in the range \(1,2,...,n^2\) such that each cell contains a different integer and the sum \(x\) of the integers in each row, column and diagonal is equal.

Let the magic constant be \(30\), how many different square grids with order \(3\) exists?

Assumptions: changing a row determines two different magic squares (e.g. changing the second row \(9+5+1\) with \(2+11+3\)) as well as invert the order of numbers (e.g. \(3+4+8\) and \(4+3+8\)); the same for columns. Furthermore there is not a limit on the maximum number inside each squares of the grid.

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