The structure of ³⁴Si was studied through γ spectroscopy separately in the β^- decays of ³⁴Mg and ³⁴Al at the ISOLDE facility of CERN. Different configurations in ³⁴Si were populated independently from the two recently identified β-decaying states in ³⁴Al having spin-parity assignments J^π = 4^- dominated by the normal configuration π(d_5/2)^-1 ⊗ ν(f_7/2) and J^π = 1⁺ by the intruder configuration π(d_5/2)^-1 ⊗ ν(d_3/2)^-1(f_7/2)². The paper reports on spectroscopic properties of ³⁴Si such as an extended level scheme, spin and parity assignments based on log(ft) values and γ-ray branching ratios, absolute β feeding intensities, and neutron emission probabilities. A total of 11 newly identified levels and 26 transitions were added to the previously known level scheme of ³⁴Si. Large scale shell-model calculations using the SDPF-U-MIX interaction, able to treat higher order intruder configurations, are compared with the new results and conclusions are drawn concerning the predictive power of SDPF-U-MIX, the N = 20 shell gap, the level of mixing between normal and intruder configurations for the 0⁺₁, 0⁺₂, and 2⁺₁ states, and the absence of triaxial deformation in ³⁴Si.