First of all, fixed assets are more commonly connected to the property plant and equipment. The PPE is mostly used for operational activities.
You can have a property that is recognized as investment property as long as you have acquired it for investment (renting etc.) and its not used for day to day operations. The treatment is different (under IFRS you can choose to hold at cost or at fair value and revalue it every year).
Intangible assets are assets that are not physical assets. So investment intangible assets are not fixed assets in the way that the term is used in accounting. At least this is the way that I would distinguish them.
I would use the term investments for cases like the following: a holding in another company, investments in securities, rental property,patents etc. etc. All these things are investments but the would not be part of the property, plant and equipment.