Linq: how to group by many-to-many relationship?

Question

I have an entity Item like next:

class Item
{
  int Id;
  string Name;
  int GroupId;
  virtual Group Group; //refers to Group table
  string Size;
  virtual ICollection<Set> Sets; //refers to many-to-many relation
}

So I want to group all items like next:

ICollection<IGrouping<string, Item>> list = AllItems.GroupBy(x => x.Group.Name).ToList();
ICollection<IGrouping<string, Item>> list = AllItems.GroupBy(x => x.Size).ToList();

And I want the same, but with Sets. Is it possible somehow?

To clarify. For example, Item1 contains in every set, then I want in the end of grouping by Sets next list:

Set 1
   Item 1
   Item 2
Set 2
   Item 1
   Item 3
Set 3
   Item 1
   Item 4
.....

Note, I need same structure ICollection<IGrouping<string, Item>> , to pass it next in code. I was thinking maybe to create intermediate structure, which can accept both ICollection<IGrouping<string, Item>> and Sets list containing my items?

Answer 1

SelectMany + GroupBy with a value selector:

ICollection<IGrouping<string, Item>> list = AllItems
    .SelectMany(x => x.Sets
        .Select(y => new
        {
            Key = y,
            Value = x
        }))
    .GroupBy(x => x.Key.Name, x => x.Value)
    .ToList();