During the Dagon Shrine quest if you pretend to be an initiate (and give all of your equipment to Harrow), you will be given your own Mythic Dawn robe and you will find that you are now an Initiate in the Mythic Dawn. If you continue to play along you will be taken to the main shrine, introduced as a new member, and asked to make a sacrifice to show your devotion to Mehrunes Dagon. If you pick up the silver dagger on the altar and kill the Argonian prisoner by the statue you will be promoted to Acolyte. At this stage you will have the Mythic Dawn appearing briefly in your in-game faction list. Other than that, this faction goes nowhere. Continuing on with the quest (or leaving Lake Arrius Caverns at all) requires that you take the Mysterium Xarxes. At that point everyone present tries to kill you, and you are kicked back out of the Mythic Dawn. There are no other quests that relate to you being a member of the Mythic Dawn, although being a member allows you to say things like "For Lord Dagon!" if you get hurt.
