Subcategories on index page

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HI ,

I wish to show the links of all products of a parent category on a single page .

How can I achieve this ?

This is what I want :-

Let's have 3 parent categories A,B,C

Furter their subcategories are a1,a2,a3 for A

b1,b2,b3 for B

c1,c2 for Parent category C

 

Then these all categories have products :-

a1 category has products :- p1ofa1, p2ofa1 ,p3ofa1

a2 category has products :- p1ofa2, p2ofa2 ,p3ofa2

 

b1 category has products :- p1ofb1, p2ofb1 ,p3ofb1

a2 category has products :- p1ofb2, p2ofb2 ,p3ofb2

 

 

Then I wish to see on my product listing page if I choose A;it should produce:-

image of first prod of p1ofa1,p1ofa2,p1ofa3

Below theseimages there must be links of products :- p2ofa1 ,p3ofa1 and p2ofa2 ,p3ofa2

 

can someone help .

Thanks,

vds