Quotient group, quotient space, and homogeneous space

Question

What are the relations between:

1. Quotient group (such as a group $G/N$),

2. quotient space, and

3. homogeneous space?

I suppose the quotient space and homogeneous space are two types of generalizations of quotient groups. But what are the similarities and differences on their properties?

• Explicit examples to demonstrate that

(1) some is one of the three kinds, but not the other two of the three kinds

(2) some is two of the three kinds, but not the other one of the three kinds

(3) some satisfies all three kinds

--- will be sufficient to claim an answer.