I am using Zenphto version 1.4.6.
When trying to creating subalbums the changes are not saved i. e. no subalbum is created. This problem is present when using Chrome or Firefox (both latest versions). When using MS Internet Explorer or Opera there is no problem i. e. I can create subalbums.

Can't remember exactly but I believe this was a bug in 1.4.6.
Please upgrade to the latest version.

Thank You for the suggestion. I will try. But after updating the last time there was a problem in openbase_dir

Without any proper error message hard to say whay. openbase_dir issues are often caused by too strict server security settings or wrong file/folder permissions.