Can't get submesh to work

I have been trying to make a mesh with multiple submeshes. But it just isn't working. I am pretty sure I did what the documentation said me to do:

     void Start () {
 
         gameObject.AddComponent<MeshRenderer>();
         MeshFilter mf = gameObject.AddComponent<MeshFilter>();
 
         mf.mesh.Clear();
         mf.mesh.vertices = new Vector3[]
         {
             new Vector3(0,0,1f),
             new Vector3(1,0,1f),
             new Vector3(0,1,1f),
             new Vector3(1,1,1f),
         };
 
         mf.mesh.subMeshCount = 2;
         mf.mesh.SetTriangles(new int[] { 0,1,2
                                         }, 0);
         mf.mesh.SetTriangles(new int[] { 2,1,3
                                         }, 1);
 }

It only shows one of the triangles. Only one of the submeshs are visible at a time. Though I set submesh count to 2. Am I doing something wrong?