Amine Nomenclature – When to use "N"
According to the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), the ‘N’ is a locant just as the ‘2’:


  P-14.3 LOCANTS
  
  P-14.3.1 Types of locants
  
  Traditional types of locants are arabic numbers, for example, 1, 2, 3; primed locants, for example, 1′, 1‴, 2″; locants including a lower case Roman letter, for example, 3a, 3b; italicized Roman letters, for example, O, N, P; Greek letters, for example, ‘α-, β-, γ-’ and compound locants, for example, ‘1(10)’ and ‘5(17)’.


Note that ‘N’ is lower than ‘2’:


  P-14.3.5 Lowest set of locants
  
  The lowest set of locants is defined as the set that, when compared term by term with other locant sets, each cited in order of increasing value, has the lowest term at the first point of difference; for example, the locant set ‘2,3,5,8’ is lower than ‘3,4,6,8’ and ‘2,4,5,7’.
  (…)
  Italic capital and lower-case letter locants are lower than Greek letter locants, which, in turn, are lower than numerals.


Identical simple substituents are indicated by multiplicative prefixes, such as ‘di’, ‘tri’, etc. The current IUPAC recommendations do not contain any rule that would stipulate that such substitutents should be grouped. By way of comparison, similar examples given in the Blue Book include names such as N,N,2-trimethyl-3-{4-methyl-3-[2-methyl-3-(methylamino)-3-oxopropyl]phenyl}propanamide.

Therefore, the preferred IUPAC name (PIN) for the compound given in the question is N,N,2-trimethylpropan-1-amine.