A code is called propelinear if its automorphism group contains a subgroup that acts regularly on its codewords, which is called a propelinear structure on the code. In the paper a classification of the propelinear structures on the Nordstrom-Robinson code is obtained and the question of extension of these structures to propelinear structures of the Hamming code, that contains the Nordstrom-Robinson code. The result partially relies on a representation of all partitions of the Hamming code into codes with parameters of Nordstrom-Robinson code via Fano planes which is given in the paper.