One of the ways you can share a public group is to embed its web maps and web applications in a ribbon gallery on a web page such as a blog or your organization's website. The group share dialog provides the HTML you need, and offers options for the layout and display of the items. All you have to do is select the options you want, then copy and paste the text into your web page or blog like we've done here.
This example uses the Community Basemaps group. Click Share, then Embed in Website to view options and obtain the embed HTML.