Accidentally pushed commit: change git commit message

In my local repo I have one commit with an incorrect commit message.

I've already published the incorrect commit message with git push.

Now the remote repo (which is GitHub-hosted) has the incorrect commit message, too.

I've already tried git commit --amend, but found that it will not work for me in this situation because I've made additional commits since the incorrect one.

How would you fix this situation?