Alongside toric varieties, flag varieties are one of the rare classes of object in algebraic geometry whose combinatorics allow for explicit computations and testing conjectures. In positive characteristics, there are "twisted" versions of these varieties, namely quotients of the form X=G/P where G is semisimple and P is a non-reduced parabolic subgroup (scheme). Their geometry significantly differs from the one of classical flag varieties; for instance, they are almost never Fano. First we will recall the classification of non-reduced parabolics and describe through examples the contractions of Schubert curves on X. This will allow us to get to a complete description of the connected automorphism group of X (as a group scheme), generalizing the classical results of Demazure.