Entryism
Entryism is a political tactic in which an organisation or group enters a larger organisation in an attempt to gain recruits, gain influence or to take control of the larger organisations' structure. This technique is commonly used by groups from the far left or right of the political spectrum to enter more centrist institutions. This is experienced more frequently in arenas where opportunities for political activity at the fringes is limited, such as two party/majoritarian systems rather than in multiparty/proportional systems where the cost of entry into the political system is lower.
Militant Tendency, a Trotskyist faction of the UK Labour Party, famously gained control of the Young Socialists and Liverpool Council before being expelled from the party in the 1980s. Another entryist technique is to join an organisation and cause a split, leaving with more members than you began with. This is the classical version of entryism advocated by Leon Trotsky in his essays on "the French Turn" in which Trotskyists entered the youth wing of the French Socialist Party (the SFIO) for a brief period in the 1930s.
Organisations which are the subject of entryism often react by attempting either marginalise or expel the protagonists.