The spell conjure animals (PHB, pg. 225) says:
You summon fey spirits that take the form of beasts and appear in unoccupied spaces that you can see within range. Choose one of the following options for what appears:
One beast of challenge rating 2 or lower
Two beasts of challenge rating 1 or lower
Four beasts of challenge rating 1/2 or lower
Eight beasts of challenge rating 1/4 or lower
On the one hand, I can see how the answer could be yes, simply because technically it is of type beast and is within the correct CR range, so RAW it should be possible to summon, say, four swarms of insects.
But on the other hand I can also see how the answer could be no, since it goes against the idea that you are summoning a specific number of beasts, and swarms are considered a "medium swarm of tiny creatures", meaning many creatures, many more than conjure animals says it can summon (i.e. the number of individual beasts in four swarms of insects is MANY more than "four beasts").
Which interpretation is correct (or is there a third interpretation)?
Note that D&DBeyond is not quite in sync with the books on this; in the description of the conjure animals spell, it lists example beasts, which include the swarms, but no such listing appears in the PHB's spell description, implying that these suggestions are the opinions of D&DBeyond's staff, not the designers (more likely it's just a listing of every monster of type "beast" for each CR).
Also, the monster entries for the swarms, say for example, swarm of rats, calls it a "Medium beast", whereas the MM (pg. 339) calls them a "Medium swarm of Tiny beasts", and all of the swarms from the Monster Manual use this wording.
However, as pointed out by V2Blast, the Monster Manual compendium page does correctly list swarms as being a "Medium swarm of Tiny beasts".
Hence I would prefer for answers to be derived from the books rather than D&DBeyond where they differ. Also note that, although I mentioned the designers above, this is not a designer-reasons question; this is a RAW question. If there happens to be a Jeremy tweet clarifying this, great! But a RAW answer is what I'm looking for if such a tweet does not exist.