Why is my regex putting a character in a different capture group than what I am expecting?

I have the given strings:

bar"{foo}"bar
bar{foo}bar

I am trying to get both the first and third capture group to be just bar. The second capture group should be {foo} both with and without quotes for each match respectively.

I have the following regex:

(^.*)("?\{.*\}"?)(.*$)

With these results:

Match 1
Full match.  bar"{foo}"bar
Group 1.     bar"
Group 2.     {foo}"
Group 3.     bar

Match 2
Full match.  bar{foo}bar
Group 1.     bar
Group 2.     {foo}
Group 3.     bar

Why are the " characters not both in the second group? I do not understand why it would be in the first if I am specifically calling it out in the second group. Do I need to tell the first group to ignore it or use it as a right bound?