When you send a message to a group, you will no longer receive a copy of the message in your inbox.
All groups created in Outlook include shared conversations, a SharePoint library, and a shared OneNote notebook, which are available to all members of that group. Group members can see any message sent to the group in the group conversations, and can continue the discussion directly from their inbox or in the group itself.
How can I see messages I send to the group in my inbox?
If you want to get a copy of messages sent to the group in your inbox, add yourself to the To, Cc, or Bcc line in the compose window.