Google is part of Alphabet. Alphabet has indeed acquired many companies via it’s holdings and subsidiaries. In several entities under the Alphabet umbrella there will be SoC teams. But AFAIK they are a part of a division not a division itself. But the startegy behind Google/Alphabet has been software until Motorola was acquired in 2011. It was seen as an entry into hardware. In retrospect, Motorola was not acquired for the hardware part, it was for the patents. Motorla was sold later but without the patents. Recently they bought part of the HTC team, the pixel part, not the VR headset team. Smartphone evolution is quite mature, the real groundbreaking stuff is over (right now) and services on the phones are now a major thing. All Android HW manufacturers no put their own services on the android phones and Google misses out. So, again the HW is not the target but the services via the hardware.
Hardware and software advisor for tech startups. ASIC, FPGA, RPi, Arduino, AI, robots, drones, blockchain, Machine learning, vision processing, IoT and 3D printers are my fields of expertise.