I wouldn't analogize them to Christianity because that's not really how doctrinal differences in Islam work. Nor am I entirely sure what the difference between a sect and a "subsect" would be (unless perhaps you mean something like how the Maronites are in full communion with the Catholic Church, to make the Christian analogy?)

That being said, yes, there are an enormous number of sects of Islam. There's a hadith attributed to the prophet which says that Islam shall have 73 sects and various lists since then have tried to compile what those 73 are, which is difficult because there have been far more than 73.

A basic list would include not just Shia and Sunni, which are probably the main splits, but also the Kharajites, from Ibadi Muslims of Oman derive but which includes a vastly larger number of extinct groups like Azraqites. Within Sunnism you have the four main schools of law the Hanafis, the Malikis, the Hanbalis and the Shafii, as well as minor schools like the Zahiri.

Shiism, which claims authority based on descent from Ali, has branched off in innumerable ways based on how precisely you define that descent. You have the various Ismaili groups which include the modern Nizari Ismaili followers of the Aga Khan as well as the Sulaymani Ismaili who are mostly in the Najran region of the Yemeni/Saudi borderlands, as well as extinct branches like the "sevener" Qarmatians. You also have in that same part of the world the Zaidi "fivers". The most populous branch are the "twelvers" of Iran.

Then you also have a large number of sort of gnostic groups claim to be Islam but, on varying scales this may or may not be disputed. This would include the Druze, who claim to be Muslims but are not typically recognized as such, the Alawites who claim to be Shia and are usually recognized as such. Then there are the Bahai's who claim to be an independent religion but that many Muslims believe to be apostates.

And on and on and on. A good book on this is W. Montgomery Watt's The Formative Period in Islamic Thought.