The structure of $^{74}$Se at low energy was investigated via spectroscopy of internal conversion electrons at the INFN Legnaro National Laboratories (LNL). A set of internal K-conversion coefficients and monopole transition strengths was measured. A large ${\rho }^2(E0;2_2^{+}\to 2_1^{+})\cdot {10}^3=210\left(130\right)$ value was deduced. This result, in addition to a low upper limit for the $0_3^{+}\to 0_2^{+}$ electron transition, casts in doubt a simple interpretation of the $^{74}$Se low-lying structure, in particular the recently proposed spherical, vibrational character. New microscopic beyond-mean-field calculations generally agree with the experimental results and are capable of producing a large ${\rho }^2(E0;2_2^{+}\to 2_1^{+})$ value, even if still a factor ≈7 smaller than the experiment. Triaxiality and a complex shape-coexistence and mixing scenario seem responsible for this unexpected experimental result.