The quotient space of U(n)/SO(m)

Question

Is there some good way to understand a quotient space of $$ U(n)/SO(m)=? $$ say $n=16$ and $m=10$?

Can it be some kind of more familiar manifold? What it is?

• The Lie algebra generators of $U(n)$ for the numerator is 256.
• The Lie algebra generators of $SO(m)$ for the numerator is 45 here.