Google Group Settings

Create the Group. Access level = Restricted.

From the Google Admin console, find the group, then click on View in Groups service. 
Then click the gear > Group settings

Go to Permissions > Basic Permission
> View Topics > All Members of the Group
> Post > All Members of Organization
> Join > Only Invited users

Go to Permissions > Posting
> Attach Files > All Members of Organization

Go to Access Permissions
> View Members > All Organization Members
> View Member Email Addresses > All Organization Members
> View Topics > All Members of the Group (should already be set from above)

Add Burke Admin to members list:
[e-mail]