Yes! On mobile only.  
In the mobile app from the Home screen, tap on the pencil icon to open your list of groups in Edit mode.  Press on the arrow icon then hold, and drag the group tiles to their new positions.  Tap the check mark icon in the upper right corner to save and exit Edit mode.  When you make these changes in the mobile app, they are reflected in the web app.
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You can also delete groups from this screen by tapping the "x" icon.

Centriq on the Web
Currently you can only re-arrange groups in the mobile app.  This feature is coming soon to the web version of Centriq. You can move items, photos, videos, documents, notes and receipts between groups, and between items in the web app.  

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Please contact us at support@centriqhome.com if you need more guidance, have questions, would like to submit a feature request or if you have other feedback.

Don't forget that you can access Centriq Online to use Centriq on your laptop or desktop computer or for optimized use on tablets.