I made a mistake with scheduling for a big meeting. The meeting was scheduled over email as a sort of 2-on-1 where my direct supervisor and I would present an idea to someone much higher up than us.
After going back and forth on the chain for a bit we set a time, but I misread the last email in the chain and entered the wrong time in my calendar. Because of distance, I missed the meeting and it went on without me.
I've already apologized to and worked with my direct supervisor to get caught up on what happened, but she wants me to schedule another meeting with the higher up so I can go over technical details with him in more detail (this was supposed to be my role in the meeting).
My question is how I should send this email (not necessarily it's content, which I believe I've already worked out). Should it be sent in the same email chain as before? Should I change the subject? Send a new email with the same subject as the previous chain? Or a new email with a new subject entirely?
(First question here, let me know if there's anything I should do to improve.)