Can I run Android virtual devices on Google Cloud or Microsoft Azure in our own subscription?

Genymotion Device Image runs the same Android virtual devices inside your own AWS, Google Cloud, Azure or Alibaba Cloud account, on your own network, and is the usual choice for enterprises already on one of these clouds; some customers run up to 50,000 devices at once. Genymotion Self-Hosted runs them on premises.

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Yes — Genymotion PaaS is available on Google Cloud Platform and Microsoft Azure, and you can create the VM in your own cloud subscription/account. Get Started with Genymotion PaaS, Get Started with Genymotion PaaS

You deploy it through the cloud marketplace, then select your subscription, resource group, region, and VM size during setup. For Azure, the docs note that only pay-as-you-go is available at the moment, and the security type must be set to Standard. Get Started with Genymotion PaaS