I'm not aware of any group being called after a kind of bats. In general there aren't that many groups for which an animal species is used as label.
NOTE: All of the following expressions are either pejorative or openly insulting!
I would have said that animals are not used for nations, for example, Frösche don't exist. The English frequently call the French froggies (and sometimes the French call themselves by this name, if there is some connection with the UK). In German they are often called Schneckenfresser (snail eaters) or Froschfresser (frog eaters).
There is only one exception - which I had never heard until quite recently, but which seems to be commonly known: Inselaffen (island monkeys/apes) for the English/British.
Bears and dragons can be used as synonyms for Russia and China, but not for the citizens of these countries.
"Organizations of people"
There are plenty of sports teams which provide an animal nickname. Examples:
- Springböcke: South African national team in rugby
- Wölfe: Members of VFL Wolfsburg (soccer)
- Adler: Members of Eintracht Frankfurt (soccer), Adler Mannheim (ice hockey)
Some other groups:
- Bullen (bulls; pejorative): police officers
- Heuschrecken (locusts; pejorative): certain kind of financial investors (as in English)
- Nachteulen (night owls): People who tend to (voluntarily) stay awake long in the evening.
- Ameisen (ants): In the context of an Ameisenheer (an army of workers in large factories), the individual workers.
- People who spend a lot of money in computer games (as in English; probably the English word is at least as widely used in German)
- (pejorative) Label for obese people
- Zecken (ticks; pejorative): An expression that is used by right-wing extremists for certain people who are politically left
- Haie (ants; pejorative):
- Kredithaie (loan sharks)
- Finanzhaie (predatory actors in the financial sector)
- Miethaie (predatory landlords)
- (probably a few more)
Many animal names are popular nicknames (e.g.: Maus, Bärchen, Hase) or insults (e.g.: Esel, dumme Kuh, Schmutzfink).
- Added Haie and another meaning for Wale.