The emerging grassroots party Barcelona en Comú won the 2015 Barcelona City Council election. This candidacy was devised by activists involved in the Spanish 15M movement to transform citizen outrage into political change. On the one hand, the 15M movement was based on a decentralized structure. On the other hand, political science literature postulates that parties develop oligarchical leadership structures. This tension motivates to examine whether Barcelona en Comú preserved a decentralized structure or adopted a conventional centralized organization. In this study we develop a computational methodology to characterize the online network organization of every party in the election campaign on Twitter. Results on the network of retweets reveal that, while traditional parties are organized in a single cluster, for Barcelona en Comú two well-defined groups co-exist: a centralized cluster led by the candidate and party accounts, and a decentralized cluster with the movement activists. Furthermore, results on the network of replies also shows a dual structure: a cluster around the candidate receiving the largest attention from other parties, and another with the movement activists exhibiting a higher predisposition to dialogue with other parties.