Partial Views are rendered within another View. The code you've shared does not show the View that contains the partial or the controller that rendered the parent View. It would help if you provided this information.
With that being said, the browser will POST to the URL in the browser's address bar when the form element does not specify an action attribute. For example, if the SubscribeMail partial is rendered within the Views/Login/Index view then the URL in the browser is /Login assuming you are not using Areas. Clicking a submit button in this situation POSTs to the /Login/Index route.
It is important to mention that nested HTML forms is invalid HTML. I can't tell from the screenshots if you have this problem or not but it is possible given the partial contains a form element. Be careful to not nest HTML forms.
Lastly, when posting question on these forums it is best to post all the relevant source code using the "code block" button because gives the community an opportunity to copy the code and run a test based on your source code.