Driving in the carpool lane without the minimum number of people or entering/exiting the lane when there are solid lines can get you a citation by law enforcement. Each time you are convicted of a moving traffic law violation in California, the court notifies the Department of Vehicle and the conviction is placed on your CA driver license record.
Our understanding of the California Vehicle Code is that there are points only for violations relating to the safe operation of a vehicle. It is not unsafe, just unlawful, to drive in the HOV lane, so that is not a point. However it is unsafe to go in or out of the lane improperly, and thus there is 1 violation point for entering or exiting a high-occupancy lane at an incorrect time (21655.8). This means driving over double lines instead of entering/exiting in the areas designated or where there is a single broken line.
According to the California bail schedule, which lists the basic fine for offenses and if a violation conviction comes with a point total, if you were written up under 21655.5(b), improper use of preferential lanes, then the fine is typically around $380 and there are 0 points assigned. The bail schedule is only a guideline and depending upon the county which you received the carpool or HOV ticket the amount you may be required to pay may be more or less than $380 listed in the schedule.