The Mythic Dawn has only two ranks that appear in your journal: 'Initiate' when you come to the Dagon Shrine and 'Acolyte' if you decide to kill the Argonian sacrifice Jeelius. Otherwise, you will be forced to leave the faction at a later stage of this quest when it comes time for your initiation.

To join the Mythic Dawn permanently, leave Lake Arrius Caverns immediately after talking to the door guard (before talking to Harrow) during Dagon Shrine. You will also gain a large disposition boost with all members of the Mythic Dawn faction, who may welcome you with the line 'Greet the new day, Brother/Sister' when approached. Although Baurus (if you kept him alive in the past quest) will give you skill increases, his disposition will be drastically diminished. The only real implications of joining the faction are that your character may gain four faction-specific combat lines (see Notes) and you will suffer a large disposition drop with all members of the Blades.

It is possible to join this faction during the quest Dagon Shrine for either a short period of time or permanently (although the latter stops you from completing the main quest).

Oblivion servant of the dawn