The bass clarinet is a transposing instrument: the Bb bass clarinet sounds a full major 9th below what is written for its sheet music. For example, that written G in the OP sounds like the F in the octave below.
The bass clarinet is nowhere close to being the only transposing instrument, though: for example, the regular Bb clarinet sounds a major 2nd below what is written (so a written C sounds like a Bb), and the French horn sounds a perfect 5th below what is written (so a written C sounds like an F). Note that transposing instruments are often labelled with what their written C sounds like (thus the "Bb clarinet" and "A clarinet" names).
(I played bass clarinet in 3 school concert bands, so I recognized that fingering for a G pretty quickly.)