Excited states in 138Ce have been studied via the 12C(138Ce, 138Ce*) Coulomb excitation reaction at 480 MeV. Relative cross sections have been determined from the gamma-ray yields observed with Gammasphere. The E2 and M1 strength distributions between the lowest six 2+ states up to 2.7 MeV enables us to identify the 2(4)+ state in 138Ce as the dominant fragment of the one-phonon 2(1,ms)+ mixed-symmetry state. Mixing between this level and a nearby isoscalar state is observed and is more than 4 times larger than in the neighboring isotone 136Ba. This is direct evidence that the stability of mixed-symmetry states strongly depends on the underlying subshell structure.