Messages sent to email alias or Group aren't in my inbox

Google only keeps one true copy of a message (it does not allow duplicates). When you send a message to yourself or to an alias that delivers to your primary address, it is only tagged with the Sent Mail label. The message will show up in Sent Mail and the All Mail, but not the Inbox.

The best way to quickly find messages sent by you is to use the Search term "from:me". If you add to that search query, you can see only messages sent from yourself to yourself: "from:me to:me"

To get these messages in your inbox, set up the alias or Group as an alternate "Send mail as" address for your account.

For more information, go to https://support.google.com/a/answer/1703601?hl=en