Depicted below is one way to divide a 6x6 square into a four areas along the grid lines such that the division has 90 degree rotational symmetry.

+--+--+--+--+--+--+
|  |              |
+  +--+--+  +  +--+
|        |     |  |
+  +  +  +  +  +  +
|        |     |  |
+  +--+--+--+--+  +
|  |     |        |
+  +  +  +  +  +  +
|  |     |        |
+--+  +  +--+--+  +
|              |  |
+--+--+--+--+--+--+

How many ways are there to quarter a square like this?