Thanks for all of your replies! I had already found the Helsingin Jyri website, but it looks quite confusing, and the only up-to-date information was about their "juoksukoulu". I don't mean to criticise a running club based on it's website, of course, but it seems hard to get in touch.
I had also found HKV on facebook, but they hadn't responded to my messages. I read their website again, however, and found an email address of the person in charge of their distance running group. He got back to me, the group is still active, and I will try to join one of their next sessions.
"Runner's Club" or "Helsingin Juoksija", to me, look more like "running as a service" - but maybe that's just the Finnish model? At least the Juoksija are also on their summer break, however, and they'll only resume in September.
I might also go to one of the "adidas runners" group runs. I have already been to a few runs with "Helsinki Running Crew", including this week, but while that's a very nice bunch of people, but of course (and as it should be), the pace is always extremely relaxed. One nice aspect of a running club, for me, has always been to run with people of different abilities, including some that were much faster than me.
Baltsu: indeed, I speak German. And, sure, I run a lot on my own, but having been part of pretty nice running clubs both in Germany and the England, I kind of miss that experience. I'm not looking to run a marathon again too soon, but if you want to meet up for a run some time, let me know - my last race was 1:21 for a half in May, so we might be running at a roughly comparable level (of course, there are worlds between 2:40 and 3:10, but two people running those times could probably still enjoy a run together...).