Poets&Writers is to the literary writing community what Writers Market is to the commercial writing community. The two sites overlap in their mission here and there but the comparison mostly holds.

Our mission? To foster the professional development of poets and writers, to promote communication throughout the literary community, and to help create an environment in which literature can be appreciated by the widest possible public.

https://www.pw.org/about-us/about_poets_amp_writers (external link)

If you’re not finding an outlet for your writing in the commercial world, check out Poets&Writers. Their database claims 1,200 literary magazines. And it’s free to access. A tremendous resource.