Joined: Jun 2014
Posts: 4,628
Likes: 943
From: Ontario, Canada
Bikes: iele Latina, Miele Suprema, Miele Uno LS, Miele Miele Beta, MMTB, Bianchi Model Unknown, Fiori Venezia, Fiori Napoli, VeloSport Adamas AX
Do you know which model of Miele it is?
As others have said, it's most likely a freewheel. Changing to a freewheel (or cassette if that's what it is) will require a longer cage rear derailleur plus a new chain to match the new cogs.
Cheers