Two different view options for index page

I want to do something that shouldn’t be too hard, but don’t seem to get my head around it: I just want to provide two different view for my index page.

My blog posts are always ordered alphabetically and in a simple text list (only the titles). In the sidebar there should be a link that says “Thumbnails” and when you click it, you see them same page, only with the thumbnails instead of the titles.

Imagine it like a file/directory program on your computer where you can choose between list-view, thumbnail-view, …

I tried to do it through the archive/s system, but it either wants me to choose a type of categorization (like ‘yearly’, so it says ‘2015’ before I can actually see the posts again), or post-by-post in alphabetical order, which is what I want, but then it only displays the posts in a simple unordered list without any option to use a template (that works the thumbnails into the second index page properly).

I use the latest version of WordPress but I still use the ‘Default’ template and re-build it form there since everything after the ‘Default’ template was far to convoluted for my usually very simple purposes. And this must be also pretty simple, right?