Begins obviously, God the Father, and creator of all, at the top. As a Catholic, that to me is the trinity. Ie, God the Father, God the Son, God the Holy Spirit. The Three in One.

If I recall there is a structure to the angles, called Choirs.

The Nine Choirs of Angels
Seraphim
Cherubim
Thrones
Dominions
Virtues
Powers
Principalities
Archangels
Angels (Regular)

These choirs are revealed throughout the scriptures of the Bibles..

Seraphim
These are the highest order or choir of angels. They are the angels who are attendants or guardians before God's throne. They praise God, calling, "Holy Holy Holy is the Lord of Hosts". the only Bible reference is Isaiah 6:1-7. One of them touched Isaiah's lips with a live coal from the altar, cleansing him from sin. Seraphim have six wings, two cover their faces, two cover their feet, and two are for flying.

Cherubim
Cherubim rank after the seraphim and are the second highest in the nine hierarchies or choirs of angels. The Old Testament does not reveal any evidence that the Jews considered them as intercessors or helpers of God. They were closely linked in God's glory. They are manlike in appearance and double-winged and were guardians of God's glory. They symbolized then, God's power and mobility. In the New Testament, they are alluded to as celestial attendants in the Apocalypse (Rv 4-6). Catholic tradition describes them as angels who have an intimate knowledge of God and continually praise Him.

Thrones
Thrones are the Angels of pure Humility, Peace and Submisssion. They reside in the area of the cosmos where material form begins to take shape. The lower Choir of Angels need the Thrones to access God.

Dominions
Dominions are Angels of Leadership. They regulate the duties of the angels, making known the commands of God.

Virtues
Virtues are known as the Spirits of Motion and control the elements. They are sometimes referred to as "the shining ones." They govern all nature. They have control over seasons, stars, moon; even the sun is subject to their command. They are also in charge of miracles and provide courage, grace, and valor.

Powers
Powers are Warrior Angels against evil defending the cosmos and humans. They are known as potentates. They fight against evil spirits who attempt to wreak chaos through human beings. The chief is said to be either Samael or Camael, both angels of darkness.

Archangels
Archangels are generally taken to mean "chief or leading angel" ( Jude 9; 1 Thes 4:16), they are the most frequently mentioned throughout the Bible. They may be of this or other hierarchies as St. Michael Archangel, who is a princely Seraph. The Archangels have a unique role as God's messenger to the people at critical times in history and salvation (Tb 12:6, 15; Jn 5:4; Rv 12:7-9) as in The Annunciation and Apocalypse. A feast day celebrating the Archangels Michael, Gabriel and Raphael is celebrated throughout the Church Sep 29. A special part of the Byzantine Liturgy invokes the "Cherubic Hymn" which celebrates these archangels and the guardian angels particularly. Of special significance is St. Michael as he has been invoked as patron and protector by the Church from the time of the Apostles. The Eastern Rite and many others place him over all the angels, as Prince of the Seraphim. He is described as the "chief of princes" and as the leader of the forces of heaven in their triumph over Satan and his followers. The angel Gabriel first appeared in the Old Testament in the prophesies of Daniel, he announced the prophecy of 70 weeks (Dn 9:21-27). He appeared to Zechariah to announce the birth of St. John the Baptist (Lk 1:11). It was also Gabriel which proclaimed the Annunciation of Mary to be the mother of our Lord and Saviour. (Lk 1:26) The angel Raphael first appeared in the book of Tobit (Tobias)Tb 3:25, 5:5-28, 6-12). He announces "I am the Angel Raphael, one of the seven who stand before the throne of God." (Tb 12:15)

Principalities
In the New Testament Principalities refers to one type of spiritual (metaphysical) being which are now quite hostile to God and human beings. (Rom 8:38; 1 Cor 15:24; Eph 1:21; 3:10; 6:12; Col 1:16; 2:10, 15) Along with the principalities are the powers (Rom 8:38; 1 Cor 15:24; Eph 1:21; 1 Pt 3:22; 2 Thes 1:7); and cosmological powers (1 Cor 15:24; Eph 1:21; 3:10; Col 2:15);Dominions (Eph 1:21; Col 1:16) and thrones (Col1:16). The clarity of the New Testament witness helps see that these beings were created through Christ and for Him (Col 1:16). Given their hostility to God and humans due to sin, Christ's ultimate rule over them (ibid) expresses the reign of the Lord over all in the cosmos. This is the Lordship of Christ, which reveals God's tremendous salvation in conquering sin and death at the cross, and now takes place in the Church. (Eph 3:10)

Angels
These angels are closest to the material world and human begins. They deliver the prayers to God and God's answers and other messages to humans. Angels have the capacity to access any and all other Angels at any time. They are the most caring and socius to assist those who ask for help.