Hybridization, introgression, or other gene flow between species means their relationships may be better described by a network than a tree. However, inferring such a network from biological data can be complicated by a second biological process, incomplete lineage sorting, which results in gene relationships that need not match any of those displayed on the network. The Network Multispecies Coalescent Model describes the combined processes, yet both practical and theoretical problems remain in using it for inference. Most recent progress in this framework has focused only on level-1 networks (no overlapping cycles). Considering the class of outer-labelled planar networks --- which may have any level --- we show that the circular order of taxon groups around each network blob is identifiable from such orders for 4-taxon subnetworks. Moreover, the 4-taxon order information can be identified from several types of data summaries, under models both with and without ILS. Finally, we give examples of blobs that cannot be distinguished, under many models and data types currently used for inference.