Two men accused of being gay received 87 lashes each for gay sex, while nine others were sentenced up to 26 lashes for adultery. Four people were caned for being drunk, including one woman who received 27 lashes.
Carried out after Friday prayers, the flogging was attended by hundreds of spectators, including children, outside the Baiturrahim Mosque in Banda Aceh, the provincial capital.
In video of the punishment seen by CNN, people can be heard jeering as the detainees, who are wearing white, traditional koko shirts, are brought up to the scaffold in front of the mosque.
Others took cellphone video of the punishment being administered by a hooded man while a voice counts the strokes over a loudspeaker. At one point a uniformed official appears to instruct the masked whipper where to land the blow.
Prior to the sentences being carried out, the detainees were given health checks and declared strong enough to undergo the punishment.
Earlier this year the governor of the province, Irwandi Yusuf, decreed that corporal sentences be carried out within the city's prison. However, the head of Banda Aceh's religious police, Muhammad Hidayat, said Friday's sentences were carried out publicly because of a lack of detailed instructions concerning the decree.
Unlike the rest of Indonesia, Aceh province follows strict Islamic laws, which make sexual activity outside marriage and same-sex relations illegal.
The HRW states that LGBT people in the state "live in a spiraling climate of fear ... (and) face ever-present harassment, arbitrary arrests and detention by Sharia (Islamic law) and municipal police, and threats of torture."
Muhammad Hidayat, the Sharia police chief, said that homosexuality was widely reviled in the deeply religious state, and that his police force would carry out the prosecution of violations of Sharia equally, without favoring officials.
Independent Indonesian news agency Witness News contributed to this report.