So I asked our administrator where should I put it. He told me that despite of it's very easy to have some Apache running on our virtual, we didn't have something like that because there's no need for it.
After short investigation I've found out that heroku.com provides free app hosting with full git support for projects based on all modern technologies. So I created my account, added my app, cloned the project and pushed my HTML site to heroku.
I expected heroku will magically consider my app to be HTML site and create apache server for it. But when I tried to push it, heroku replied: "Push rejected, no Cedar-supported app detected". Heroku also thinks that nobody needs it.
Luckily, Heroku supports php applications, so all we need to do is to fool heroku a bit - mimic a php application by simply create empty index.php file:
and turn php engine on apache off:
echo 'php_flag engine off' > .htaccess
When you add these two files to the app you have static site hosted on heroku.com.
Neat, isn't it?