set formation from different subsets

Let's say that I have the following subsets:

{1},{2},{3},{4},{3,4},{2,4},{1,3},{1,2},{1,2,4}

I want to form sets using these subsets where all numbers will be covered but the subset selection will be different.

Numbers can be used only once in a set(selecting {1,3} and {3,4} for the same set is not allowed since 3 is in both subsets).

Example sets to be formed: set1={{1},{2,4},{3}}, set2={{1,2},{3,4}} etc.

How can I code this?

Thank you.

[KALYAN ACHARJYA]

How many sets to be formed?

Also set1={1},{2},{3},{4},

set2={3,4},{1,2}

set3={2,4},{1,3}

set4={1,2,4}

is this OK?

[Ezgi]

Sets will be:

set1: {1},{2},{3},{4}

set2: {1},{2,4},{3}

set3: {1},{3,4},{2}

set4: {1,2},{3},{4}

set5: {1,2},{3,4}

set6: {1,3},{2,4}

set7: {1,3},{2},{4}

set8: {1,2,4},{3}

set9: {1},{2},{3,4}