LINQ select all items of all subcollections that contain a string

Question

I'm using jqueryui autocomplete to assist user in an item selection. I'm having trouble selecting the correct items from the objects' subcollections.
Object structure (simplified) is

public class TargetType
{
    public int Id { get; set; }
    public string Name { get; set; }

    public virtual ICollection<SubCategory> SubCategories { get; set; }

    public TargetType()
    {
        SubCategories = new HashSet<SubCategory>();
    }
}

public class SubCategory
{
    public int Id { get; set; }
    public string Name { get; set; }
    public virtual ICollection<SubTargetType> SubTargetTypes { get; set; }

    public SubCategory()
    {
        SubTargetTypes = new HashSet<SubTargetType>();
    }
}

Currently I'm doing this with nested foreach loops, but is there a better way?
Current code:

List<SubTargetResponse> result = new List<SubTargetResponse>();
foreach (SubCategory sc in myTargetType.SubCategories)
{
    foreach (SubTargetType stt in sc.SubTargetTypes)
    {
        if (stt.Name.ToLower().Contains(type.ToLower()))
        {
            result.Add(new SubTargetResponse {
                Id = stt.Id,
                CategoryId = sc.Id,
                Name = stt.Name });
        }
    }
}

Answer 1

You can do using Linq like this

var result = myTargetType.SubCategories
                         .SelectMany(sc => sc.SubTargetTypes)
                         .Where(stt => stt.Name.ToLower().Contains(type.ToLower()))
                         .Select(stt => new SubTargetResponse {
                                        Id = stt.Id,
                                        CategoryId = sc.Id,
                                        Name = stt.Name });

The above query doesn't work. The following should work, but I'd not recommend that as that'd not be faster or more readable.

var result = myTargetType.SubCategories
                         .Select(sc => new Tuple<int, IEnumerable<SubTargetType>>
                                            (sc.Id, 
                                             sc.SubTargetTypes.Where(stt => stt.Name.ToLower().Contains(type.ToLower()))))
                         .SelectMany(tpl => tpl.Item2.Select(stt => new SubTargetResponse {
                                        Id = stt.Id,
                                        CategoryId = tpl.Item1,
                                        Name = stt.Name }));