Is the set inside a set subset of the bigger set?

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I just started set theory (ncert maths 11th grade) and it had a question:

Let $A = \{1 , 2 , \{3,4\} , 5 , 6\}$

Is $\{3,4\}$ a subset of A?

The book said no. I think the answer should be yes, since $A$ contains a set which contains the elements $3,4$ hence $A$ contains $3,4$ and by the definition of subset $\{3,4\}$ should be a subset of $A$.