Context. HC_3N is a molecule that is mainly associated with Galactic star-forming regions, but it has also been detected in extragalactic environments. Aims. To present the first extragalactic survey of HC_3N, when combining earlier data from the literature with six new single-dish detections, and to compare HC_3N with other molecular tracers (HCN, HNC), as well as other properties (silicate absorption strength, IR flux density ratios, C_(II) flux, and megamaser activity). Methods. We present mm IRAM 30 m, OSO 20 m, and SEST observations of HC_3N rotational lines (mainly the J = 10–9 transition) and of the J = 1–0 transitions of HCN and HNC. Our combined HC_3N data account for 13 galaxies (excluding the upper limits reported for the non-d...