Measurement of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>e</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>e</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:mo stretchy="false">→</mml:mo><mml:msup><mml:mi>π</mml:mi><mml:mo>+</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mo>−</mml:mo></mml:msup><mml:msup><mml:mi>π</mml:mi><mml:mn>0</mml:mn></mml:msup><mml:mi>η</mml:mi></mml:math> cross section below <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msqrt><mml:mrow><mml:mi>s</mml:mi></mml:mrow></mml:msqrt><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mtext> </mml:mtext><mml:mtext> </mml:mtext><mml:mi>GeV</mml:mi></mml:mrow></mml:math>

The process ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}\ensuremath{\eta}$ is studied in the center-of-mass energy region below 2 GeV with the SND detector at the VEPP-2000 ${e}^{+}{e}^{\ensuremath{-}}$ collider. The following four intermediate states contribute to this process: $\ensuremath{\omega}\ensuremath{\eta}$, $\ensuremath{\phi}\ensuremath{\eta}$, ${a}_{0}(980)\ensuremath{\rho}$, and a structureless ${\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}\ensuremath{\eta}$ state. We measure the total ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}{\ensuremath{\pi}}^{0}\ensuremath{\eta}$ cross section and the cross sections for its components: $\ensuremath{\omega}\ensuremath{\eta}$, $\ensuremath{\phi}\ensuremath{\eta}$, and a sum of ${a}_{0}(980)\ensuremath{\rho}$ and the structureless state. Our results are in agreement with previous measurements and have comparable or better accuracies.