I’ve grown multiple Facebook groups into businesses with thousands of users as clients.

Use a multi-channel marketing approach that targets external communities that revolve around your group topic.

Post into the group with a Content strategy for building brand influence. You can do this by attributing Cialdini to each of your posts and then monitoring engagement. This serves as a self-assessment of which influence principals are leading your brand forward in your community so you can major in those principals and align your content to what appeals your community most (the Facebook insights may actually confuse you about what works and sucker you into advertising the wrong direction. You need to build an organic strategy based on the natural needs and desires of your community first. This is akin to “voice of customer” best practices.)

You might also consider an inbound approach within your multi-channel marketing strategy, with all channels pointing to your Facebook group, essentially your landing page, which is associated with a relevant domain name.