This is why work friendships in my experience are quite easy, even for an introverted hermit like myself. Often common interests between people, and _tons_ of time bonding.
If i really cared about forming more friendships i'd do what you suggested - find groups that interest me and spend the time needed to form friendships. I'm also a little weird in that while i get along with a lot of people and i am (hopefully) easy to get along with, i'm generally not interested in relationships without common interests and activities. Because i don't like to socialize purely for the sake of socializing - i like building something together, or playing something together, or enjoying food together, or whatever it is i am actually interested in.. which is usually software.
[1]: Which is probably useless, as i'm generally an introvert who still has less friends than i'd prefer.