Islamic State thugs are committing harrowing crimes against Yazidi women and girls in Iraq, including organized rape and sexual assault — and in one case, chose women by drawing names in a “lottery,” according to a report by Human Rights Watch.

The barbaric acts are war crimes and may be crimes against humanity, said the group, which conducted research in the town of Dohuk early this year and interviewed 20 women and girls who escaped the clutches of ISIS.

“Those fortunate enough to have escaped need to be treated for the unimaginable trauma they endured,” said Liesl Gerntholtz, women’s rights director at Human Rights Watch.

The fanatics captured several thousand Yazidis in northern Iraq’s Nineveh province in the summer of 2014. Witnesses said the young women and girls were separated from their families and other captives, then moved from place to place in Iraq and Syria.

The 11 women and nine girls the rights group interviewed had escaped between September 2014 and January 2015.

Half, including two 12-year-old girls, said they had been raped — some several times and by several of the militants.

Nearly all said they had been forced into marriage; sold, in some cases a several times; or given as “gifts.” They also described seeing other captives being abused.

A Dohuk doctor who treated female survivors said that of the 105 women and girls she had examined, 70 appeared to have been raped.

All of the women and girls interviewed showed signs of acute emotional trauma — and several said they had attempted suicide while in captivity or witnessed suicide attempts by others to avoid rape, forced marriage or forced religious conversion, the report said.

The terror group has tried to justify its sexual atrocities by claiming that Islam allows sex with non-Muslim “slaves” — including beating and selling girls.

One woman, identified as “Rashida,” 31, said she used a fighter’s phone to call her brother after she was abducted. She told him she was being forced to convert and marry — so he told her he’d try to help but that if he couldn’t, she should kill herself because “it would be better than the alternative.”

“Later that day, they [ISIS fighters] made a lottery of our names and started to choose women by drawing out the names,” she said. “The man who selected me, Abu Ghufran, forced me to bathe, but while I was in the bathroom, I tried to kill myself. I had found some poison in the house, and took it with me to the bathroom. I knew it was toxic because of its smell. I distributed it to the rest of the girls and we each mixed some with water in the bathroom and drank it. None of us died but we all got sick. Some collapsed.”

In another case, 12-year-old “Wafa” told Human Rights Watch that she was captured with her family in the village of Kocho, where she was separated and taken to Raqqa in Syria.

She said an older fighter assured her she would not be hurt, yet he repeatedly raped her.

“He was sleeping in the same place with me and told me not be afraid because I was like his daughter,” she said. “One day I woke up and my legs were covered in blood.”

Wafa eventually escaped, but her parents, three brothers and sister are still missing.