HTML form send data by GET instead POST

The problem is rather common and the answer quite elusive:

Somewhere in your code you have an orphaned <form>. This means that the next form is nested in the previous one, and its method is ignored. Delete or close the superfluous <form> and you are done.

It should be a post (assuming that you forgot the closing tag only in your example). I added your code and put the closing tag in an html file and submitted in Chrome. This is what I see in the network trace:

Also look at this question in case you are doing the same.