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Plastic deformation of the brittle C14-Fe2Nb Laves phase occurs mostly by basal slip due to the complex crystal structure. Here, we compare the barriers for basal slip for the known mechanisms of direct slip, synchroshear and undulating slip using density functional theory calculations. According to our calculated generalized stacking fault (SF) energies, the most favorable mechanisms are synchroshear and undulating slip. Both mechanisms lead to stable SF with a formation energy of 50 mJ/m2 through the same unstable SF configuration at the transition. The energy barrier of approximately 3 J/m2 indicates a low dislocation mobility as expected from the brittle character. We also determine the influence of vacancies and antisite defects on the formation energy of stable and unstable SF. Both kinds of point defects tend to lower the energy barrier on both sides of 2:1 stoichiometry. This explains the experimentally observed off-stoichiometric softening of C14-Fe2Nb. The small energy differences between the Fe2Nb Laves phase polytypes raises the question if there are further deformation mechanisms with low barrier. Therefore, we additionally consider the known transformations between C14, C15 and C36 Laves phases by successive synchroshear as further deformation mechanism. Our calculations for polytypic transformations by successive synchroshear steps show that the corresponding energy barriers are in fact very similar to the energy barrier for basal slip in C14. This suggests that the energy needed to create a stable SF in C14 by synchroshear is also sufficient to initiate polytypic transformations where existing SFs in C14 are further transformed to form C15 or C36 Laves phases.