Being Part of a Group

I listened with interest to an ad on the radio asking listeners if they feel alone since the family has grown up and left home. It says get together with other people and have a chat over a cup of tea or coffee. Then they announce where to go if you are over age 60. Does this mean if we are under the age of 60 we aren't supposed to feel alone and our kids should still be at home? Are our lived supposed to be so full we don't have time for others? I hear of different groups like Garden Circle, Womans Division, Lions Club etc but I have no idea exactly what these groups are all about or even how you become part of these groups.
I've never had a large circle of friends and not real sure how you end up with them or even if I would want to. I've been to cafe's quietly sitting on my own having a latte seeing a group of women having lunch together, talking and laughing and it looks like they are having a good time but once again I sit wondering how does someone become part of that culture.
Quite a few years ago I thought playing golf would be a good way to get exercise and meet other women. I knew someone that belonged to the local golf club and I mentioned a few times that I'd like to learn how to play hoping to hear a reply of hey that's great come on down to the course on club day and check it out. After 10 years waiting for that invite I pretty much had given up. Then one day out of the blue one of the Mothers at my kids school mentioned the local golf club was looking for new members and asked I would like to play golf. I was so excited at last I was going to get that long awaited opportunity. That first day club members supplied well used golf clubs that looked like they belonged in a museum but I didn't care cause I was finally part of a group and I was going to play golf and hopefully make some new friends. I found the women to be friendly enough and they seemed to be interested in who I was. After that first day I went out and bought a second hand half set of clubs and got right into playing. Turns out I was pretty good at hitting a ball. Then again being 39 I was the youngest player, the oldest was 79. Within 6 months I bought a new set of clubs and my handicap just kept coming down. By this time I realised the women all wanted to know who I was but didn't really want to know me so there were no new friends made but I was content just being outside getting exercise and playing a sport I really enjoyed. After about 3 years I ended up going back to work and the clubs sat in the garage gathering dust. There were no phone calls inviting me to come have a game and playing 18 holes on my own doesn't really appeal.
Once again I am not working and my days seem to pass quickly but I can't say they are full. I make lists of things to do so I at least feel I am accomplishing something. I don't hold onto hope that the phone will ring and someone on the other end will be calling to invite me out for a game of golf, lunch or even a coffee but if it happened I'd put down my list and I'd be there just to be part of a group.