  We revisit Langlands' construction of the Taniyama group to define a plectic
Taniyama group for any totally real field F. The construction is functorial in
F and recovers Langlands' original Taniyama group when F = Q. We relate our
construction to Nekovar's 'hidden symmetries' in classical CM theory,
generalising the relationship between the Taniyama group and Tate's
half-transfer maps.
