A CREW WAS DISTRACTED LOOKING FOR GND TFC AT SAT AND THEN SWITCHED TO CHKLIST COMPLETION. THEY TAXIED OFF THE END OF TXWY W THINKING THEY COULD CONTINUE TO TXWY G. NO SIGNS INDICATED A TURN ON TO TXWY H REQUIRED.

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WE WERE INSTRUCTED ON TAXI OUT TO GIVE WAY TO A B737 FROM OUR R. SO WE BEGAN OUR TAXI FROM OUR RAMP TO RWY 12R VIA TXWY W THEN TXWY H. WE SAW B737 APCH FROM THE R BUT THEY WERE ON TXWY G AND WERE NOT A FACTOR (GND DID NOT SAY WHAT TXWY B737 WAS ON). WE WERE RUNNING THE TAXI CHKLIST ON TXWY W AND MY EYES WERE LOOKING DOWN AT THE ELECTRONIC CHKLIST ON MY MFD. WHEN I LOOKED UP I SAW GRASS STRAIGHT AHEAD AND SAID SOMETHING TO THE CAPT WHO STOPPED THE ACFT. THE ACFT'S MAIN GEAR WAS IN THE GRASS ABOUT 2 FT FROM THE PAVEMENT. GND CTL WAS CONTACTED AND COORD BTWN THE ARPT AUTH AND COMPANY BEGAN. THE ACFT WAS LATER MOVED WITH NO DAMAGE TO THE GEAR OR STRUCTURE AND THERE WAS NO DAMAGE TO ARPT PROPERTY. IN HINDSIGHT; I CAN SEE THE CONFUSION AT NIGHT BTWN THE TRANSITION FROM TXWY W TO TXWY H. IT LOOKS AS THOUGH YOU CAN CONTINUE STRAIGHT AHEAD TO TXWY G. THERE SHOULD BE A SIGN OF SOME SORT; LIKE A RWY DIRECTION SIGN; WHERE TXWYS W AND H MEET. THERE IS EVIDENCE OF SKID MARKS AT THIS INTXN FROM OTHER ACFT WHO HAVE ALMOST CONTINUED STRAIGHT AHEAD.