174 (one hundred [and] seventy-four) is the natural number following 173 and preceding 175.
There are 174 7-crossing semi-meanders, ways of arranging a semi-infinite curve in the plane so that it crosses a straight line seven times. There are 174 invertible (0,1)-matrices. There are also 174 combinatorially distinct ways of subdividing a topological cuboid into a mesh of tetrahedra, without adding extra vertices, although not all can be represented geometrically by flat-sided polyhedra.
The Mordell curve has rank three, and 174 is the smallest positive integer for which has this rank. The corresponding number for curves is 113.