Terrorist groups like the Islamic State of Iraq and Syria (ISIS) have exploited social media such as Twitter to spread their propaganda and to recruit new members. In this work we study the extent to which ISIS is able to spread their message beyond their immediate supporters. Are they operating in their own sphere with limited interaction with the overall community? Or are they well rooted among normal users? We find that three-quarters of the interactions ISIS received on Twitter in 2015 actually came from eventually suspended accounts raising questions about the potential number of ISIS-related accounts and how organic ISIS audience is. Towards tackling these questions, we have created a unique dataset of 17 million ISIS-related tweets posted in 2015. This dataset is available for research purposes upon request.