As per section 3 of the Companies Act 2013 , You Can form three types of Companies.
1) Public Ltd Company
2) Pvt Ltd Company
3) One person Company
1) Public Ltd Company Can be formed either
a) Company Ltd by shares or
b) Company Ltd by Guarantee or
c) An unlimited Company
Public Ltd Company required minimum 7 or more members to form , minimum paid up Capital required is 5Lacs and 3 Director are required
2) To form Pvt Ltd Company minimum members required 2 numbers , Minimum director's 5 number and maximum 15 number , Minimum paid up Capital required is 1 Lac .
3) One person Company can be formed by one person, one Director minimum and Capital of Rs 1 Lac minimum.
4) Foreign Company has been define under section 2(42) of the Companies Act 2013 as any entity that has been incorporated outside India ,
Happens to have a place of Business in India either physically through any other agent / electronic or digital means
Business activities are conducted by the entity in any other manner .
5) Government Companies means any company in which not less than 51 % paid up share Capital held by the Central or State Government ,