Meetup is great to organise your local meetup. Meetup also has great sharing and API options. They do support embeding the meetup group together with the next meetup. However, there is no out-of-the-box support to embed your schedule to another website.
This is a Sinatra project that solves this issue by accessing the Meetup API and simply rendering an HTML table.
Code and examples can be found here: https://github.com/munen/meetup-calendar