By the 'Dog of Egypt' was one of Plato's favourite exclamations, probably with referance to Anubis, but i'd like to question whether this also would have refered to Sirius/Dog star.
The connection with Anubis and Sirius/Dog star is easily made, there is the noted 70 day period of invisibility which is considered to be associated with the 70 day preperation of the the mummiform Sah, and this work is carried out by Anubis, and thus the 70 day Sirius periodic is relevent to his cult.
Ovid and Vergil referred to Sirius as Latrator Anubis, representing a jackal- or dog-headed Egyptian divinity, guardian of the visible horizon and of the solstices, the Egyptians had represented the star as a dog.
It is difficult to see how in the later period and classical times the Dog-star had also become associated with Isis-Sopdet, yet it appears that from the early classical period Orion had become associated with Horus, as mentioned by Plutarch.
This was quite an easy and straightforward mythological comparative for the period, as Horus could be seen as a mighty hunter and warrior, as Orion was seen also as in the classical world, and yet from there to also associate Orion with Osiris was far more problematic.
Given though that the association of Orion with Horus/Osiris had been made, Isis then appears to be given the role of companion to the constellation, in the role of the Dog, a very widespread cultic association of the later period therefore associating Isis with dogs, even riding upon them.
It must be questioned though whether the earlier pyramid texts suggest this diminished supportive role of Isis to Osiris, as his dog, or whether this has simply derived from Horus becoming associated with Orion, and the rest of the Horus/Osiris/Isis mythos being relocated to the constellation in accordance.
It has also been suggested in recent times by Egyptologists that the Sokar Feast of Khoiak was celebrated relevant to the seasonal appearance of the constellation Orion, given this, then any association of Sokar with Orion would gradually have translated into an association of Orion with Osiris, given the mergance of Osiris-Sokar, and the rise of the former and diminishing of the latter.
Morph.