No one I have discussed this with is aware of a previously created symbol for normal subgroup.
It certainly seems to have the function of a comparison symbol. Our suggestion is to devise a shape in the style of the other triangles listed in Rule XVI (NC page 113-114) using the letter n to identify it as "normal" -- [braille]$t.n] A tn must describe the shape the symbol represents ("equilateral triangle pointing left").
As a comparison sign, it would require a space on either side.
Section 107 covers this situation. Just use a shape symbol followed unspaced by 2 letters.
So your symbol could be [braille]$ns for "normal subgroup" which is a shorter term than modifying a triangle. Your tn (or special symbols page) would still have to describe the print sign (left-pointing equilateral triangle) when defining the symbol's meaning.