On one hand left & right varies from country to country and time to time, and can therefore mean various things. On the other hand there is one main thread that goes through most of them: The promotion of government control vs private control. In other words: Collectivism vs Individualism. The left tends to be the side which promotes more government control, the right tends to be the side which promotes less government control.
This means the proper abstract spectrum would be (from left to right):
[Communists] [Socialists/Social Democrats] [Nationalists] [Conservatives] [Libertarians] [Anarchists]
Where do Fascists and National Socialists fit on that spectrum? Well, certainly not near Libertarians. As deep collectivists and authoritarians they find their place on the left, even though it is common knowledge that they aren't. But that has to do more with Marxist leaning academics trying to defend Communism by trying to place it as the opposite of Fascism, even though both ideologies have a lot of similarities (for example both fundamentally oppose Libertarianism, just as vice versa).
As such, one could argue the label "right wing", "alt right", "far right" also serve the purpose to undermine Libertarian (pro free market, pro individual liberty) positions by insinuating that a reduction of socialism is equal to the rise of Fascism.
One further nuance is that in every society there is an Overton Window. If a given society is already deep in the left spectrum, the range of acceptable parties and views are all on the left. In such a society, there is no place for Libertarians, not even for (actual) Conservatives. Those on the relative right are therefore not even right wing, even though they are labeled as such. The only thing that matters is that the parties rather represent directions which they intend to shift society towards (similar to vectors).
Libertarians are inherently individualists and as such promote individual liberties along with individual responsibility. This has roots beyond mere economics - it's based on the non-aggression principle: Do not initiate force against others. They recognize that governments and states continually infringe on the rights of individuals, including taxation. The less taxes a government has, the smaller it is. The smaller the government, the less impact it has regardless what policies are enacted. Anything that goes towards the "left" would mean it would grow the government and diminishes the prevalence of Libertarianism in the given society. So if it were too "left-wing", it would cease to be Libertarian by the very nature that the state apparatus would grow too much. Anything that would go towards the "right" would decrease state power, and enact the principles of Libertarianism more consequently.
The answer is therefore: Libertarians are, on a proper, abstract spectrum, the true right-wing, possibly even far right.
And the "far right" that is known today are just a different iteration of the left wing, who just oppose (neo-)Marxism, but are still somewhat in favor of socialism. But to be fair, the term "far right" and "alt right" are buzzwords meant to smear ideological opposition as evil by conflating them with Nazis, regardless of what policies they entail.
The other answer is, with the premise that the left-right spectrum is unresolvably convoluted, that their place is outside of it - or rather that the potential stretch of the left-right spectrum decreases as Libertarianism is more enacted, and at the theoretical peak of it (Anarcho-Capitalism), it would shrink to zero (no government, no politics, only individual preference and action matter).
Edit: The third, more accurate answer is combined with my personal political model: There are 3 main directions of politics, and all views can be mapped on it.
Globalism: Any political pursuit to enact policies which act outside of its borders. Be it expansionism, interventionism, imperialism, open border policies, immigration, financial aid, multiculturalism.
Localism: Any political pursuit to enact policies which act to enforce borders, sovereignty, economic independence, isolationism, and the maintenance of the country's representative culture, tradition and religion.
Libertarianism: Any political pursuit to reduce the power and role of the state and to increase individual liberties along with individual responsibilities.
All three directions are in contradiction to its principles, and all three can be combined. In fact, all existing parties inhabit various degrees above zero of all three.
A key role has the vertical line. The more authoritarian the given society, the more impact the government has (or can have). As you approach Libertarianism (towards to bottom), the less impact any government leaning (left or right) has (be aware, in this context "left" and "right" mean something different than above!). So naturally if you reach Anarchy, there is no political leaning to exert - it's entirely up to the individual what it financially supports or not. Also the vertical line reflects the magnitude of taxation and state debt.
Examples: The Soviet Union started somewhere around the top, and wandered further upwards and towards Globalism. After it engulfed East Europe and ceased its expansion (because it had to), it started to wander slightly towards Localism again.
North Korea is a good example of a country which ended up as a highly isolationist, authoritarian regime, placing it to the top-right.
National Socialism started out on the top-right, and wandered somewhat towards Globalism as it started WWII and pursued the Holocaust as extensively as possible.
Conservatism is placed between Localism and Libertarianism, Social Democracy is placed between the center and the top left, the USA started off at the bottom.