The answer to this question is sort of complicated because of disagreement on how to define the terms, specifically, who is considered to have been killed "on purpose", rather than simply dying in the course of war. Some of the lower-end figures (as few as 5 million non-Jewish deaths) use a more stringent definition of that terminology, while some higher end figures (ranging up to 11 million) use a more expansive definition. There's also the issue of not having exact death tolls for some groups of people, particularly within the occupied Soviet Union.

That said, the United States Holocaust Memorial Museum gives the following figures for non-Jewish victims of Nazi Germany:

Soviet civilians (non-Jewish): 5.7 million

Soviet POWs: 3 million (50,000 of whom were Jewish)

Polish civilians (non-Jewish): 1.8 million

Roma (Gypsies): 250,000-500,000

Disabled: 250,000

Criminals and "asocials": 70,000

Jehovah's Witnesses: 1,900

Homosexuals: hundreds to thousands (potentially counted under "asocials")

So that adds up to about 11,000,000. Add in the 6,000,000 Jewish deaths, and you get a figure of around 17,000,000, which is generally considered the "high end" figure for deaths under Nazi occupation.

A few notes on those figures:

The figure for Soviet civilians is a difficult one to calculate, since determining what was a "deliberate" civilian death as a result of racial policy vs. a "normal" civilian death in the course of war is somewhat arbitrary. As a result, different authors have given widely disparate figures for civilian deaths in the USSR.

The figure for Soviet POWs is somewhat controversial; some Soviet/Russian historians give lower figures, as low as 1.8 million (Krivosheev), while German authors give higher figures, as high as 3.3 million (Streit). Generally, Western scholarship has defaulted to the higher figures, which are based on German archival records, and 3.3 million is generally treated as the "authoritative" total for Soviet POWs. I'm not sure why the USHMM opted to round that down to 3 million. This is my area of expertise, so if you want more details here, I can definitely provide them.

The figure for Polish civilians is generally well-accepted among Western authors, with most estimates at or just below 2,000,000; however, the Polish Institute of National Remembrance gives a higher figure of 2,770,000.

The German Federal Archives reported in 2003 that 200,000 people died as a result of the Nazi "euthanasia" programs (Aktion T4 and Aktion 14f13), in which disabled patients in German institutions were murdered. However, there were additional killings of disabled patients in occupied Poland and the occupied Soviet Union as well, which means the number of disabled people killed is certainly higher than that 200,000 figure. Research here is ongoing, and it's also unclear how many of those deaths are already counted in the Polish/Soviet civilian death tolls. (As you've probably noticed, possible double-counting of people who fall into more than one victim group is another confounding issue here.)

The figures for Roma are also controversial and will likely never be able to be calculated with precision. Exact figures for the prewar Roma population are hard to come by, so death tolls are similarly hard to calculate. Some authors give lower-end figures in the 150,000 range, while activists have argued for totals above 500,000, which are probably not realistic. Most authors have reached figures within the range listed by the USHMM (mainly toward the lower end), but that's why there's such a significant uncertainty there.

Finally, we know that between 5,000 and 15,000 people were sent to concentration camps for homosexuality, but we don't know how many of them died; nobody has done a precise study, although some activists have argued that the figure may have been as high as 60%; again, this also runs into the problem of double-counting, since people sent to concentration camps for homosexuality would have been classified as "asocials".

So, as you can see, calculating these kinds of figures is a complicated and problematic process, and we'll probably never be able to answer your question with a high level of precision. It's frustrating as a historian not to be able to give exact answers to what ought to be black-and-white questions, but it is what it is, unfortunately. Hopefully this was at least somewhat helpful, and if you have more specific questions you can always follow up with me.

Sources:

The figures I cited above were from the USHMM's Holocaust Encyclopedia, which can be found here. See also the USHMM Encyclopedia of Camps and Ghettos, vols. 1-4 (Indiana UP, 2008-2022).

Dieter Pohl, Verfolgung und Massenmord in der NS-Zeit 1933–1945 (WBG, 2003)

Wojciech Materski and Tomasz Szarota, Polska 1939–1945. Straty osobowe i ofiary represji pod dwiema okupacjami (IPN, 2009)

Christian Streit, Keine Kameraden: Die Wehrmacht und die Sowjetischen Kriegsgefangenen 1941-1945, 3rd ed. (JHW Dietz, 1997)

Grigory F. Krivosheev, Soviet Casualties and Combat Losses in the Twentieth Century (Greenhill, 1997)

Günter Lewy, The Nazi Persecution of the Gypsies (Oxford UP, 2000)

[this is obviously nowhere near an exhaustive list of relevant sources, just the ones I pulled from immediately]