Show only nodes that are connected via entity reference with views
Contextual filters work combined (AND), so if you define two or more contextual filters, all of them have to pass.

Here's what I would do.


Use Pathauto to create a pattern for your group content, e.g. g/[node:nid].
Create additional aliases for long name and short name.
Make your view work with just the NID contextual filter and use the block display type.
Configure your block to only show up on group node type and place it in main content. 


Alternatively, you can also use Panels to create a similar node page for group nodes. To create the additional URL aliases for each group, you might want to try NodeSymLinks module.