It's using RSA with key length of 2048 bits [1], and one can assume that both prime factors have equal bit length [2] i.e. 1024 bits each, and so the size of all the other private components can be derived from that. I don't know what OpenSSL's in-memory format is for this data, I suppose therein lies a good part of the challenge!
I.e., is it a 8192-bit AES256 key?