Unitary group of order six U(6) having three sub groups.
Type 1. U(6)⊃ U(5) ⊃ O(5)⊃ O(3) ⊃ O(2)
Type 2. U(6) ⊃SU(3) ⊃ O(3) ⊃ O(2)
Type 3. U(6) ⊃O(6) ⊃ O(5) ⊃ O(3) ⊃ O(2)
How these chains are produced.
three sub algebra of Unitary group (6) as 1. U(5) .
2. SU(3)
3. O(6)
here the three chains in attachment is attached.
I want to know how these chains are understands in group theory.