This is a belated answer that may not help the original author but may help someone in the future.
I think my Mira shower head is a Mira Logic and it's built into the wall with a type of joint for movement. The head looks similar to the 415.
I took it apart by pulling off the outer ring (normally used to adjust the type of jet) which hides the fact its in two halves. This came off easily I think I just twisted and pulled it towards myself.
You can then clearly see it's in two moving halves
Then I got a flat head screwdriver and inserted it between the moving two halves and twisted.
A little click on two sides and it came apart. You can then clean it.
Matt Baker
November 2013