One accusation against the Church is that they can then get away with making graven images.
There is no official Catholic division of Ten commandments. The Catechism of the Catholic Church states:
The division and numbering of the Commandments have varied in the course of history. The present catechism follows the division of the Commandments established by St. Augustine, which has become traditional in the Catholic Church. It is also that of the Lutheran confessions. The Greek Fathers worked out a slightly different division, which is found in the Orthodox Churches and Reformed communities. (CCC 2066)
The Catechism states that it uses the Augustinian grouping because it is traditional and it rhymes easily which makes it easy to memorize. (CCC 2065) Catholics thus have liberty of conscience in determining which division of the Decalogue they believe best. That is there is no correct way to group the ten commandments.
Catechism also argues that The Decalogue (Ten Commandments) forms a coherent whole. Each "commandments" refers to each of the others and to all of them; they reciprocally condition one another. To transgress one commandment is to infringe all the others. (CCC 2069) So, grouping of the commandments does not matter as long as all 10 are held together.
The main two differences in the division of the Ten commandments are:
Grouping of commandment against other gods and idols:
Idols are only of interest to God insofar as they are false gods. God has no problem with statues in general, or even religious statues. It is only because they are considered to be gods that the Lord is interested in them as this violates his territory. God himself has commanded Israelite to build statues (Exo 25:18). If God had problem with Idols Per se, then how can God ask them to violate his own commandment?
By dividing the no false gods and no idols as two commandments like:
Commandment 1: You shall have no other gods before me.
Commandment 2: You shall not make for yourself a graven image, or any likeness of anything that is in heaven above, or that is in the earth beneath, or that is in the water under the earth; you shall not bow down to them or serve them; for I the LORD your God am a jealous God, visiting the iniquity of the fathers upon the children to the third and the fourth generation of those who hate me, but showing steadfast love to thousands of those who love me and keep my commandments. [emphasis added]
The latter would be almost eight times as long as the former; Commandment 1 is 5 words long in Hebrew, while the next is 39 words long. Please note that the italicized part of Commandment 2 makes no sense if it is for making idols alone. As God has no reason to be jealous of an idol if it is NOT worshiped as a god equal to Him (which is the Commandment 1).
Coveting a neighbor's wife and desiring his property be grouped together or not?
The Deuteronomy 5 version of the Ten commandments uses different verbs for these commandments. It says one must not "covet" your neighbor's spouse, but that one must not "desire" a neighbor's property. Two separate verbs, thus reasonably considered as two separate commandments.
See: The Division of the Ten Commandments by James Akin
The Order of the Commandments in the Catholic Faith are ordered by the most grievous- to the least grievous.
The above answer makes several errors in transcription. Using the link provided one can see what is true: The Decalogue in the Church's Tradition
2064 In fidelity to Scripture and in conformity with the example of Jesus, the tradition of the Church has acknowledged the primordial importance and significance of the Decalogue.
2065 Ever since St. Augustine, the Ten Commandments have occupied a predominant place in the catechesis of baptismal candidates and the faithful. In the fifteenth century, the custom arose of expressing the commandments of the Decalogue in rhymed formulae, easy to memorize and in positive form. They are still in use today. The catechisms of the Church have often expounded Christian morality by following the order of the Ten Commandments.
2066 The division and numbering of the Commandments have varied in the course of history. The present catechism follows the division of the Commandments established by St. Augustine, which has become traditional in the Catholic Church. It is also that of the Lutheran confessions. The Greek Fathers worked out a slightly different division, which is found in the Orthodox Churches and Reformed communities.
2067 The Ten Commandments state what is required in the love of God and love of neighbor. The first three concern love of God, and the other seven love of neighbor.
As charity comprises the two commandments to which the Lord related the whole Law and the prophets . . . so the Ten Commandments were themselves given on two tablets. Three were written on one tablet and seven on the other.27 2068 The Council of Trent teaches that the Ten Commandments are obligatory for Christians and that the justified man is still bound to keep them;28 the Second Vatican Council confirms: "The bishops, successors of the apostles, receive from the Lord . . . the mission of teaching all peoples, and of preaching the Gospel to every creature, so that all men may attain salvation through faith, Baptism and the observance of the Commandments."29