It's actually really straightforward.
- Start of input
- Followed by any number of groups of 4 characters from [A-Za-z0-9+/],
- Followed by one of the following:
- [always matches]
- Four characters where
- The first and second match /[A-Za-z0-9+/]/
- The third matches /[AEIMQUYcgkosw048]/
- The fourth is a "="
- Four characters where
- The first matches /[A-Za-z0-9+/]/
- The second matches /[AQgw]/
- The third and fourth are both a "="
- Followed by the end of input
It's probably a bit simpler after the update I just did for you:
- Start of input
- Followed by any number of groups of 4 characters from [A-Za-z0-9+/],
- Followed by zero or one of the following:
- Four characters where
- The first and second match /[A-Za-z0-9+/]/
- The third matches /[AEIMQUYcgkosw048]/
- The fourth is a "="
- Four characters where
- The first matches /[A-Za-z0-9+/]/
- The second matches /[AQgw]/
- The third and fourth are both a "="
- Followed by the end of input