In Bleach, while Ichigo and the gang invading Hueco Mundo, they keep cutting away to Rurichiyo Kasumioji and her story:
they save her, kill the guys with the Hollow Swords, and save the head captain.
When did that really happen? Did they help her before or after going there?
It's a filler arc, that does not contain canon material. The anime creators were forced to insert this new arc randomly in the middle of the Hueco Mundo arc as the anime was catching up too fast with the manga.
However, I think it's safe to say that it occurs in the tiny window between Ichigo's training and Orihime's kidnapping, as Ichigo uses his hollow abilites, and Orihime hasn't been kidnapped yet.
I believe it occurs after Hueco Mundo because Chad gains his other arm's ability there and he uses it in the filer arc when he is helping to protect Rurichiyo.
This tells me that it either occurred after the Hueco Mundo arc, or it happened parallel with it and was not canon.
I choose to believe it is canon despite what other people say because Rurichiyo and Kenryu are some of my favorite characters from Bleach.
This arc is what is called "filler." It is, as the name states, an arc or story line created by the animation team to "fill" time whilst waiting for the manga to progress further into the story so that the animation team can continue to produce the story. It is not canon.
However, to answer the question that you posed, the arc takes place, chronologically speaking, after the Sousuke Aisen arc, but before the Fullbringer arc.
Additionally, the "replacements" arc, in which a treasonous member of the research and development squad (12) creates mod-soul copies of the shinigami, is also a filler arc, and is non-canon.
It has to happen while they are in Hueco Mundo because Chad can use del Diablo and Ichigo still has his soul reaper powers. Thinking on that, it’s impossible for this to be after Hueco Mundo because Aizen is done with.
