Of the religions (and cultures), the most famous to have the swastika-style symbol with four legs were Buddhism and Hinduism. The swastikas (sometimes under different spellings or names) would look like the symbol on the tail of the plane or its mirror image.
The easiest way to tell if it is the type of swastika used by the Nazi Party is to look for an "S" in the symbol, which is the right-facing, or clockwise, form. Although they generally rotated it 45° (so the center would form an "x" rather than a "+"), it also appeared with no angle.