Subdivisions of the Zodiac
The Hellenistic Astrologers subdivided the domiciles into smaller sections. The ones that have survived till the present day are the Decans (10 degree segments, so three decans comprise each sign). These are not widely used and when they are, it it often a modern system, which assigns the decans to the rulers of the triplicty of which they comprise. For example Aries decans being ruled by Mars, Sun and Jupiter.
There were more than one system of decans in Hellenistic times but the one that was most used assigns the decans to the planets in Chaldean (Babylonian) order, starting from Mars ruling the first decan of Aries. The sequence thus goes Mars, Sun, Venus, Mercury (first decan of Taurus), Moon, Saturn, Jupiter (first decan of Gemini) Mars, and so on repeating the seven planet cycle throughout the zodiac. ending with Mars ruling the last decan of Pisces. There is a clear order and pattern to this system.
The other sub dignity which was if anything more widely used was the Bounds or Confines. This system does not have an obvous order or system except that one of the malefics, Mars or Saturn rules the last Bound of each domicile. There are 5 bounds per sign but they don't have equal sizes, nor is the pattern of sizes regular. Only 5 planets are used (which might explain why there are 5 bounds per sign) - the two lights, Sun and Moon do not have bounds anywhere in the zodiac.
The 'system' used seems to come from semi-mythical astrologers named Nechepso and Petosiris, who allegedly were an Egyptian King and a High Priest. The system of bounds was therefore called the Egyptian bounds.
The Astrologer Ptolemy tried to tidy up this system, along with Astrology generally and introduced a system of bounds which he says he found in an ancient manuscript and was more logical. Whether or not he did find it that way, his bounds never caught on till the Seventeenth Century. William Lilly and other astrologers 'rebelled' against some of the material coming from the Arab Astrologers and mounted a back to Hellenistic campaign. Unfortunately the only Hellenistic text they had was Ptolemy and they therefore mistakenly took Ptolemy as the original system of Astrology. In fact Ptolemy was a deviant, and the Astrology of the Arabs was more in tune with actual Hellenistic practice than Ptolemy was.
The final division I'll mention is the 'twelfth parts' or Dodekatemoria. (spellings vary). This seems only to be used occasionally and there are again several variants. I may mention them later on if I feel the need