A regular hexagon with sides of length $6$ has an isosceles triangle attached to each side. Each of these triangles has two sides of length $8$. The isosceles triangles are folded to make a pyramid with the hexagon as the base of the pyramid. What is the volume of the pyramid? If the answer is in the form $a\sqrt{b}$, what is the value of $a$?

Let's think step by step and output the final answer within \boxed{}.
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