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We show that certain two-term transformation formulas between basic hypergeometric series can easily be described by means of invariance groups. For the transformations of nonterminating φ23 series, and those of terminating balanced φ34 series, these invariance groups are symmetric groups. For transformations of φ12 series the invariance group is the dihedral group of order 12. Transformations of terminating φ23 series are described by means of some subgroup of S6, and finally the invariance group of transformations of very-well-poised nonterminating φ78 series is shown to be isomorphic to the Weyl group of a root system of type D5.

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