When you deploy public groups with a change set, any nested group structure is not retained in the target organization.
Nested groups are created by adding a public group as a member of a different public group. This nesting is saved to the GroupMember object and is considered to be data, and can be created and deleted using the Data Loader.
Change Sets are only able to deploy metadata. They can be used to deploy the group definition, but not the members of the groups.
The nested group needs to be added as a group member again in the target organization.
See also
Components Available in Change Sets
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