Suicide was very common during the holocaust among all groups of people. It was common among Jews, Germans, and anyone who felt death was better than what they faced in the future. Some suicides even included entire families. First, I will begin with suicides among Jews.

It was very common among Jews who feared what the Nazis could do to them. They felt their death would be better than whatever fate the Nazis had planned for them. Those whose committed suicide did it in their homes, in ghettos, and concentration camps. But most occured within concentration camps and ghettos where conditions were poor and the people imprisoned within them were already being worked to death.

The conditions and treatment of concentration camp prisoners often led to their deaths... as well as their mental state. Some argue that those who survived were more inclined to have hope or perhaps they had someone close to them like a sibling, relative, or friend that kept them alive. They had a stronger mental state than someone who was all alone.

The prisoners were treated awfully: they were starved, beaten, tortured, and forced to work as slaves. The poor conditions led to illness, starvation, tiredness etc. In some concentration camps, the fear of death existed as well in the form of gas chambers, random death selections, and so forth. But death occured in nearly every concentration camp and being surrounded by death - seeing corpses piled up, the smell going far past the concentration camp, and losing someone... it is torture to the prisoners. Many viewed death as their only relief and many wished they would die to end their suffering.

Prisoners would commit suicide by jumping off buildings, running into electrified fences, giving a guard a reason to shoot them.... and many deaths were covered up as suicides too. Prisoners often had a deteriorating mental health in concentration camps. Seperation from family, loss of hope, depression, anxiety, fear.... all these factors mixed in someone who later committed suicide in the camps.

Nearly all prisoners that survived dealt with mental health issues after the war. PTSD was common and even after the war, several survivors committed suicide. The treatment for mental health was not the same as it is today. There was a lack of knowledge and resources... hence why many survivors never really spoke of their experience until one day they felt they should.

The next group of suicide was among resistance members, though this was often for their cause. Resistance fighters, if captured, some would kill themselves instead of letting the Nazis get their knowledge after torture. Those who killed themselves after getting captured were viewed as heroes by those they left behind.

The second largest group was Germans themselves in the final days of the war. The most known suicide is Hitler himself. But many other high ranking Nazi officials also committed suicide, including Joseph Goebbels, who also killed his entire family, including his six children. They feared having to face justice for war crimes and knew the penalties would be harsh.

High ranking officials weren't exempt. Lower ranking officials also committer suicides as well as camp guards, sonderkommando and kapos, even people who supported the Nazi party. If they feared the fate they would get was worse than death, they often chose death over paying for their crimes.

Nazi sympathizers also committed suicide in Nazi occupied countries in the final days of the war. Many people who suffered under the Nazis also committed suicide, including prisoners of war, poles, jehovah's witnesses, homosexuals, and so forth.

So overall, suicide rates went up during the war, mostly because people feared whatever fate awaited them was worse than death, but there were many other factors mixed in.

Sources:

Suicide in Inmates in Nazis and Soviet Concentration Camps: Historical Overview and Critique López-Muñoz & Cuerda-Galindo

Suicide in the Nazi concentration camps Medical Review Auschwitz

This older answer may be of interest to you.