The plane of the solar system, called the Ecliptic which runs along the Zodiacal belt of constellations, is tilted about 60 degrees to the plane of the Milky Way. The two points where these two planes intersect on the sky are in the constellation Sagittarius near the Lagoon Nebula ( Messier 20), and on the border between Taurus and Orion near the open cluster NGC 2129.
There is, by the way, no physical reason why these two planes should be identical. Stars have their rotation axis pointed at random in space, and the plane of the solar systems that orbit them should also be oriented pretty much at random with respect to the Milky Way.