Why doesn't shift + select let me select multiple objects to group?

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You can only group Draw objects together, but an image in Writer is a Writer object. You can first insert the image in Draw and then copy it there and paste it into your Writer document. That way it becomes a Draw object and shift+click will extend the selection and you can group it (context menu).

Or you group all those objects in Draw and paste the whole group to the Writer document. You can then enter the group (context menu) and drag the parts to where you need them.

You can follow the problem in https://bugs.documentfoundation.org/s... and its duplicates.