  We provide a simple parametrization for the group G2, which is analogous to
the Euler parametrization for SU(2). We show how to obtain the general element
of the group in a form emphasizing the structure of the fibration of G2 with
fiber SO(4) and base H, the variety of quaternionic subalgebras of octonions.
In particular this allows us to obtain a simple expression for the Haar measure
on G2. Moreover, as a by-product it yields a concrete realization and an
Einstein metric for H.
