A Question About Clutch Handbags.?

I know this is a strange question,
I've never had a clutch bag before but I got one to go with my dress for my college graduation. I'm not certain about the etiquette for when you're carrying one.
We're going out for a meal after the ceremony, I usually put my bag on the floor but I don't know what to do. It's fairly bug for a clutch. Should I leave it on the ground f on the table next to me?
I normally don't stress over strange things like this but my whole family will be there and they're strict about table manners.

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