How many major parts are there to NFPA 101?

There are 43 chapters and 4 annexes in NFPA 101.

As for "major parts", you could consider the following general divisions:

• Chapters 1-4, 6-11 and 43 referred to as "fundamental" or "base chapters"
• Chapters 5 Performance based options
• Chapters 12-42 Specific occupancy chapters
• Annexes A and B containing useful additional information

(based upon preface of 2009 edition)