Social attributes of intelligent robots are important for human-robot systems. This paper investigates influences of robot autonomy (i.e., high versus low) and group orientation (i.e., ingroup versus outgroup) on a human decision-making process. We conducted a laboratory experiment with 48 college students and tested the hypotheses with MANCOVA. We find that a robot with high autonomy has greater influence on human decisions than a robot with low autonomy. No significant effect is found on group orientation or on the interaction between group orientation and autonomy level. The results provide implications for social robot design.