If your site is using unique permissions at subsite level, following might work. I am explaining it for a single group IT:
[1] Add content editors in your welcome page of root lelvel site.
[2] Set chrome type to none, and set all it sharepoint groups in audience
[3] set content to
<script type="text/javascript">window.location.href='/IT/';</script>
Same way add content editor web part for each subsite.
This way, if someone from IT group logs in, then and then the content editor web part become visible and the script redirects them to IT home page. This is just a hint, not a real solution.
Draw backs:
[1] Admins will also redirect to the same page and no one will be able to edit the page.
[2] Someone having permission to access more than one department will redirect to any site randomly based on script execution order.
There are ways to improve script written in content editor web part to overcome both of the above changes. You can simply using sharepoint javascript api to improve the script.
Let me know if this makes sense.