In 2002, Walter Trump created the first trimagic square. It has order 12 and is therefore the smallest possible trimagic square.
The original square was created by the specified author and these are absolutely different squares. From this original square n!!/2 squares can be created by applying symmetric row-column-permutations. In a strict sense, these are therefore not new squares. So for order 12 we will get 12!!/2=23040 squares.
In 2018, Walter Trump created 33 more trimagic squares that are completely different from the original square and thus can not be generated from them by row-column permutations.
All algorithms are described in detail in my PDF book. (chapter: Trimagic Squares)