Procession Order for Special Masses?

I am not sure what the other groups that you mention are, however, according to a source called, The Church Visible, here is the order:

Precedence of Papal Awards:
Supreme Order of Christ
Order of the Golden Spur
Order of Pope Pius IX
Order of St. Gregory the Great
Order of St. Sylvester
Cross Pro-Ecclesia et Pontifice
Benemerenti Medal

Ecclesiastical Procession:
Knights of Columbus (as Honor Guard)
Thurifer
Crucifer
Seminarians
Diocesan Priests
Monsignori
Concelebrants
Visiting Prelates
Auxiliary Bishops
Holy Sepulchre & Malta
Malta & Holy Sepulchre
Knight of St. Sylvester & Knight of St. Gregory
Commander of St. Gregory & Comm. Of St. Sylvester
Knight of the Pian Order & Comm. Of Pian Order
Prelates in Choir
Ordinary
Ordinary's attendants

For "regular" processions the General Instruction of the Roman Missal, 3rd edition, number 120 and Ceremonial of Bishops, number 128 say:

Thurifer with thurible / burning incense (if incense is being used)
Ministrer with Cross - between two ministers with candles
acolytes
other ministers (e.g., lectors)
deacon with book of the gospels (or lector in deacon's absence)
(other deacons, 2x2)
(concelebranting priests, 2x2)
Presider (bishop) or for regular Masses, priest

If presider is bishop, is followed by:

other assisting deacons
ministers who assist with the book, miter, and pastoral staff