This seems to be very confusing to many players. Obviously our music education is being ignored!
Just to keep the unknowing from posting something wrong:
Low C is below the staff.
Third space C is just that.
High C is two ledger lines above the staff.
Double C is one octave above that.
Octaves start with C. This means that Double G is higher than Double C.
For the sake of confusion: our double C is merely a high Bb for a flute.
There is very LITTLE musical content written for unamplified Double C.