@Clay Kolden - Security Analyst Thanks for posting in our Q&A.
Based on my research, only security-enabled Microsoft 365 Groups are supported in intune. So, the groups that you don't see may not be security-enabled Microsoft 365 Groups. Here is some information about adding a new group in intune:
https://learn.microsoft.com/en-us/mem/intune/fundamentals/groups-add#add-a-new-group
https://learn.microsoft.com/en-us/entra/fundamentals/concept-learn-about-groups#group-types
Hope it will give you some ideas.
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