There are many, many, many groups that all say they are Christian yet they have such differing views on what that is that they will not worship together. Is Islam the same? Roughly, how many groups of Islam are there that will not worship with other groups? Are some of them hostile or violent to each other like the Catholics and Protestants in N. Ireland?
I will start by quoting this hadith :
Narrated AbuHurayrah: The Prophet (PBUH) said:
As you can see the prophet already said that Islam will also split into too many sects. Such as Sunni,shiite,Abadthi etc...
However the most dominant is the sunnis (~90% of muslims) and then followed by the shiite (~10% of the muslim population) and the rest is divided between other sects.
Anyone of these sects can be a hostile sect if they want. There is not sect that encourages its followers to be hostile. But its the followers who take advantage of their sect to start attacking others.
For example, some Sunnis may create a group called X and this group will start attacking Y hence Y will start blaming the sunnis because X belong to the sunni sect.
I hope this simple answer would give you some idea about the groups in Islam
As Suhaib said, the major divisions are Sunni and Shiia. Sufism is sometimes considered another division, but some Sufis identify as being Sunni or Shiite. Different schools of thought also exist within those divisions, however it does not interfere with followers worshiping together. There are also some groups who identify as Muslim or include Islamic tradition but are not included in the greater Muslim community.
There's a brief history of the divisions and schools of thought on the New World Encyclopedia.
The divisions of Islam differ greatly from those of Christianity in that followers are unified in their obligation to perform a pilgrimage (hajj) to Mecca. Despite sectarian conflict, the Saudi government grants visas to pilgrims from countries who would not typically be allowed into the country. Sectarian conflict began in the division between Sunni and Shiia (a brief account can be found in the previous link), and continues today. Although it is integrated in political strife, there are sectarian debates in Saudi/Iranian relations, civil conflicts in the Gulf countries, and the war in Syria, to name a few. The hajj is sometimes disrupted by sectarian conflict, but the intention is to unify Muslims from around the world.