Multithreads of fftw on 2D matrix's transform

Question

I wonder the principle of multithreading fftw on 2D matrix, if fftw uses multithreads to transform every row of the matrix.If not, i want to use multithreads to conduct 1D fft on the rows of matrix in parallel to accelerate the transform.

I have try many fft libraries, and fftw should be the most known and stable one to conduct fft on 2D matrix.However, I want to know if the fftw's multithreads in its document has accomplish the parallel transform on every row of the matrix.