  Departing from the observation that the Penrose limit of AdS_3 x S^3 is a
group contraction in the sense of Inonu and Wigner, we explore the relation
between the symmetric D-branes of AdS_3 x S^3 and those of its Penrose limit, a
six-dimensional symmetric plane wave analogous to the four-dimensional
Nappi--Witten spacetime. Both backgrounds are Lie groups admitting bi-invariant
lorentzian metrics and symmetric D-branes wrap their (twisted) conjugacy
classes. We determine the (twisted and untwisted) symmetric D-branes in the
plane wave background and we prove the existence of a space-filling D5-brane
and, separately, of a foliation by D3-branes with the geometry of the
Nappi--Witten spacetime which can be understood as the Penrose limit of the
AdS_2 x S^2 D3-brane in AdS_3 x S^3. Parenthetically we also derive a simple
criterion for a symmetric plane wave to be isometric to a lorentzian Lie group.
In particular we observe that the maximally supersymmetric plane wave in IIB
string theory is isometric to a lorentzian Lie group, whereas the one in
M-theory is not.
