lighter socket question

quick question: i have a heated jacket with a connection that looks like it goes into a cigeratte lighter.

thing is it doesnt fit snug into the 12v socket i have on the bike… just falls out.

is there a much smaller type of 12v socket or are there adapters avai?

the socket looks like this…



Never seen anything like that before for plugging into a 12v socket. Unless someone knows better I’d suggest you snip it off and put a proper one on?

thanks for the reply!

i’ve just found out that it is a DIN or hella type connection - managed to find an adapter on ebay…