I just don't get what is happening. I can create just about any template group name and it works fine, but if I try to create a template group called "themes", I receive the 403 Error Directory access is forbidden. The index.html file just has "test 123" in it, so no coding issue. I have checked my files, and nothing else is called "themes". I may have had themes.html in my root at one point, but that was deleted days ago, so not sure if something is holding onto that and creating some conflict. Is there anything else I can look at or try since I do want to use this as my subdirectory, www.mysite.com/themes?
If you are using EE 3-6 (possibly lower as well) "themes" is a protected name in the EE Installation at the web root of your install. So mydomain.com/themes is seeing that directory before your template directory and throwing the 403 error. Either choose a different name for your template group or do as JCOGS suggested.
EE stores useful CSS and JS resources used by EE itself and some add-ons in the directory
/themes - so I imagine any attempt to define a template group with that name will cause problems.
Why your attempts to create a
themes.group template folder give you a 403 is unclear to me (rather than some more meaningful error) but suspect that it is EE's way of letting you know that there is a conflict.
I don't know whether it is possible to rename the
/themes directory, but it is certainly possible to move it. So a work-around would be to add an extra directory to the webroot called (say)
cats and move the
/themes directory to be below this - and then update the relevant entries in EE's URL Paths and Settings CP page to point at the new location (i.e.
/cats/themes). Then you will avoid the conflict ...