Why does Logitech Group not connect to the large monitor?

Judging by your description, this has nothing to do with the Logitech Group, if I understood correctly, the other monitors are not recognized on your screen. This may have to do with the fact that they are not recognized by the laptop at all. Press the Windows key + P once and try to expand or duplicate your screen. If that doesn't work, right click on the desktop and go to the display settings. There you click on detect if the monitors are detected. If the monitors are not recognized, you should check your cabling. You can also change the HDMI cable or DP cable to check if it is a defective cable. Can you connect directly to the monitor with a cable? Are the connections working there. Try to adjust the settings for HDMI on the monitor. Sometimes switching to a different HDMI version can help. Reset your monitor to factory settings to avoid configuration errors.