Hindutva, the core political ideology of India's current ruling party, the Bharatiya Janata Party (BJP), seeks to transform constitutionally secular India into a Hindu Rashtra (`Hindu nation'). Although Hindutva has all of the features of right-wing extremism (RWE), it is nevertheless viewed as a sociopolitical phenomenon due to the Eurocentric nature of RWE discourse. Recent theoretical and analytical research has sought to showcase the similarity between RWE and Hindutva, whereas empirical research on their relationship has not been conducted. To fill that gap, in our study we collected 15 million tweets, and in network analysis, identified prominent themes of RWE, including exclusionary nationalism, conspiracy theories, and anti-minority violence and hate speech among the supporters of Hindutva and BJP. Furthermore, our toxicity analysis performed to understand which themes produced higher levels of toxicity, we found that Hindi-language tweets related to conspiracy theories and anti-minority violence or hate speech were more toxic than English-language tweets. Given that the growing global presence and normalisation of RWE-based ideas and movements are sources of concern for political science researchers, our research broadens the discussion on RWE in the Indian context and invites researchers to further investigate Hindutva from the perspective of RWE.