Digestive efficiency traits are promising selection criteria to improve feed efficiency in pigs. However, the genetic relationships between digestive efficiency and sow reproductive traits are mostly unknown and need to be estimated. In this study, reproductive traits were available for 61 601 litters recorded on 21 719 Large White purebred sows. The traits were comprised of the number of born alive (NBA) and the number of weaned piglets (NWP), the number of stillbirths (NSB) and piglet mortality during suckling (PM). For a subset of 32 518 litters, the mean (MBW) and CV of piglet birth weights (CVBW) were deduced from individual piglet weights as well as the proportion of piglets weighing less than 1 kg (PPL1K). Growth and feed efficiency traits were available for 4 643 Large White male pigs related to sows with reproductive performances. They comprised average daily gain (ADG), daily feed intake (DFI) and feed conversion ratio (FCR). A subset of 1 391 pigs had predictions for digestibility coefficients (DC) of energy, organic matter and nitrogen obtained by analysing faecal samples with near-infrared spectrometry. Estimated heritabilities were low for NBA, NSB, NWP and PM (0.08 ± 0.01 to 0.11 ± 0.01) and low to moderate for litter weight characteristics (0.14 ± 0.02 to 0.38 ± 0.01). Heritability estimates were moderate to high for ADG, DFI and FCR (0.37 ± 0.04 to 0.54 ± 0.05) and moderate for DC traits (0.26 ± 0.06 to 0.38 ± 0.07). Genetic correlations were low between ADG, or alternatively FCR, and reproductive traits. They were significantly different from zero with MBW (0.19 ± 0.06 with ADG and 0.15 ± 0.06 with FCR) and PPL1K (0.19 ± 0.07 with ADG and 0.18 ± 0.07 with FCR). All genetic correlations between DFI and reproductive traits were low and not significantly different from zero. Genetic correlations between DC traits and NBA were significantly different from zero for DC of organic matter and energy (<0.25 ± 0. 11). DC traits were moderately correlated with MBW (>0.30 ± 0.11), CVBW (<0.36 ± 0.11) and PPL1K (<0.37 ± 0.11) at the genetic level. Genetic correlations between DC traits and PM were significantly negative and hence favourable (<0.38 ± 0.12). Finally, genetic correlations between DC traits and NWP were close to zero. These results suggested that sows closely related to growing pigs with the best digestive efficiency would produce heavier and more homogeneous piglets, with slightly smaller litter sizes at birth but better survival. Hence, there is usable genetic variation in DC that could be exploited to define new selection strategies in maternal lines aiming at improving not only feed efficiency but also piglet survival.