Discretization methods for differential-algebraic equations (DAEs) are considered
that are based on the integration of an associated inherent ordinary differential equation (ODE).
This allows to make use of any discretization scheme suitable for the numerical integration of ODEs.
For DAEs with symmetries it is shown that the inherent ODE can be constructed in such a way
that it inherits the symmetry properties of the given DAE and geometric properties of its flow.
This in particular allows the use of geometric integration schemes with a numerical flow
that has analogous geometric properties.