To configure your notification settings, open WhatsApp for web or desktop > Menu > Settings > Notifications. Here you can:
You can also mute individual chats. Click on a chat > Menu > Mute > and select the preferred amount of time. To turn notifications back on, find the muted chat and click Menu > Cancel mute.
Note: If you mute a group or an individual chat on your phone, it will also be muted on WhatsApp Web/Desktop. All other notification settings are independent of your phone and computer and do not affect one another.