L1 Transfer within company from one branch to another

[visa_2014]

I worked with U.S. subsidiary in India for 3 years and then moved to US on L1A.

Currently, I am working with U.S. subsidiary on L1A for more than one year and want to know if I can move to parent company without any visa changes. This means is it possible to move from U.S. subsidiary to US Parent with same visa i.e L1A

If this is possible, I would like to understand the things which would come into picture for this process?

Also, can parent company apply for my GC once my visa is transferred to parent company?

Thanks