As you mention that the notification comes and goes within a second, I think that it's actually a WhatsApp notification which says "Checking for new messages" - a screenshot of that notification can be found in this MIUI thread. It is not related to your groups, muting them will not make any difference.
I've occasionally seen it myself; it appears and disappears extremely quickly.
If you want to verify what the notification actually is, check your phone's notification log which can be viewed by creating a settings shortcut to the log on the desktop using your launcher of choice.
I've seen speculations that it only appears if your internet is spotty, or if WhatsApp cannot work in the background for whatever reason (eg Data Saver is on, your phone/ROM is extremely aggressive with background tasks like MIUI is or because of low RAM). Another notification which appears under similar conditions is "You may have new messages", but that messages stays permanently until you open WhatsApp.
As for how to disable it without stopping all other WhatsApp notifications, it would natively only be possible in Android Oreo because of support for notification channels. I think the relevant channel for the notification is "Other Notifications". I've disabled that channel and I haven't seen the notification in ages (then again, can also be because I've never met the conditions for seeing the notification ever after).
I should also warn you that disabling the channel also turns off other notifications like "WhatsApp Web is running" - check everything carefully!