The only rotation axis obvious to me is rotation by 360 degrees, the identity. Vertical mirror planes I've been dicing and cutting it through several planes and I still see none. Yet, the structure looks fairly symmetric and I feel like I'm missing something.
No center of inversion either.
Not too terribly sure about horizontal mirror planes. I suppose that one bisecting the plane horizontally would be there but I am not entirely sure if this is appropriate.
Right now I'm saying this structure belongs to the C1 point group.