Loop and page

I need a page that would output all the subcategory from a specific category and each start a loop for all posts present in their own categories.

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Title

Category I
{ *loop* [ post I ] [post II ] [ post III ] }

Category 2
{ *loop* [ post I ] [post II ] [ post III ] }

(etc.)
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I’ve tried to manually put all theses category in the same page (at least, putting a new subcategory would require little time to set up) but it seems like loop aren’t working in a page. I want to avoid creating a custom template with static codes if I can…