How do I move items within the same listview to another position in large icon view?

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C#2.0

C#

C#3.5

ListView

I have a Windows Forms ListView in C# and I have setup the large icon view.
I also set autoarrange to false and allowdrop to true. Now I would expect that I can freely move a large icon ListViewItem within my ListView control. That's not the case. I was go through all settings of the ListView again and found nothing more relevant that would make me able to move single icons to another place within my ListView. I don't need any DragDrop nor from outside or from another control, just to clarify. I only want to move an existing item a bit more left or right within the listView window without dragging it on any other items. Free position movement was always no big deal in large icon listViews, so what am I missing?

What I have tried:

I checked over all properties of the listView again. I have one large symbol in my listView which I want to move to another place within the listView. the listView contains no more symbols that this one and will not contain more than one. I want to change the position within the listView from the one and only item!
I found only Dragging and Dropping codes which rely on the exact selection of one or more items. I cannot move my item freely with it and the codes weren't working at all for me. I do not Drag'n Drop something in my ListView or out of it.
There must be another way of doing this!