Are such groups as Salafis, some Sufis, the Muslim Brotherhood…etc. those referred to in the Hadeeth narrated on the authority of ‘Abd Allaah ibn ‘Amr: "And my Ummah will be divided into 73 groups…." [At-Tirmithi]?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

There is no doubt that harmony and unity are far better than disagreement, and that disagreement is criticized in most cases. This is indicated by many verses and authentic, clear Hadeeths.

We mentioned in another Fatwa (ruling) that the criteria for good disagreements, should be, Allaah willing, like those of the prominent scholars of Islamic jurisprudence. Refer to that Fatwa as it includes a detailed account of this. 

As for the Hadeeth referred to by the questioner, it apparently and most likely does not refer to these groups because the disagreement which the Hadeeth refers to is the disagreement that occurs about fundamentals of religion and it involves deviation from the way of Ahlus-Sunnah Wal-Jamaa‘ah (the Sunni mainstream), such as that of the Al-Jahmiiyyah, Al-Qadariyyah, Al-Murji’ah sects and the likes of them.

Imaam Al-Qaraafi stated that these sects are actually called “sects” in the sense of "divisions", because they contradict the saved sect in what concerns the very meaning of religion or in one of the principles of Sharee'ah, and not in subsidiary areas.

Irregular issues of detail do not result in disagreements that divide people into parties and groups. Division occurs only when the disagreement involves universal and fundamental issues. 

And Allaah Knows best.