Vyxal 3, 23 bytes

{:1>|:KᶻṄȮȮ÷⁾Ḣh$Ȯ÷}Wᶻ2<

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Perl 6, 83 bytes

my&f=->\n {my \p=min grep {n%%$_&!is-prime $_|n/$_},2..^n;Inf>p??flat p,f n/p!![n]}

Note: uses the is-prime builtin

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Javascript (ES6), 94 bytes

n=>{for(a=[],d=2,l=q=0;n>1;)n%d?d++:(n/=d,q&&(a[l++]=q*d),q=q?0:d);q&&l&&(a[l-1]*=q);return a}

Ungolfed:

n=>{ //function declaration
  for(
    a=[], //the list
    d=2, //current factor
    l= //next index of the list
    q=0; //stored factor
    n>1; //while n>1
  )
    n%d? //if the factor is not a factor of current n
      d++ //go to next factor
      :( //else
        n/=d, //remove the factor
        q&& //if a factor is stored,
          (a[l++]=q*d), //add multiple of the saved factor and current factor
        q=q?0:d //store factor if it doesn't exist
      ); //end else
   //implicit for loop close 
  q&& //if there is remaining factor
    l&& //if the input is not a prime
      (a[l-1]*=q); //place the factor in the last element in the list
  return a //return the list
} //end function

05AB1E, 8 bytes

Òā¨ÉÅ¡P¦

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Explanation:

            # implicit input (example: 72)
Ò           # prime factorization ([2, 2, 2, 3, 3])
 ā          # indices ([1, 2, 3, 4, 5])
  ¨         # drop the last element ([1, 2, 3, 4])
   É        # is odd ([1, 0, 1, 0])
    Å¡      # split on 1s ([[], [2, 2], [2, 3, 3]])
      P     # product ([1, 4, 18])
       ¦    # drop the first element ([4, 18])
            # implicit output

Note that this correctly returns [] for prime inputs.

Haskell, 106 104 101 bytes

c x=2/=sum[1|0<-mod x<$>[1..x]]
(x:r)%n|c x,mod n x<1,d<-div n x,c d=x:g d|1<3=r%n
e%n=e
g n=[4..n]%n

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Less golfed and explanation:

c x = 2 /= sum[1|0<-map(mod x)[1..x]] -- counts number of divisors of x and returns true for all non-primes

g n = f [4..n] n            -- call f with a list of factor candidates and n

f []    n = []              -- if there are no factor candidates, return the empty list
f (x:r) n                   -- for the factor candidate x ...
    | c x,                  --    check if x is composite
      (d,m) <- divMod n x,  --    set d = n div x and m = n mod x
      m < 1,                --    n is divided by x if m = 0
      c d                   --    check that d is composite or 1
    = x : f (x:r) d         -- if all those checks are true append x to the list and determine the composites for d
    | otherwise = f r n     -- otherwise check the next candidate

JavaScript ES6 112

c=n=>{with(a=[]){for(i=k=1;i++<n;)for(;1^n%i;n/=i)push(++k%2?pop()*i:i);k%2||push(pop()*pop());return k<3?[]:a}}

test=k=>{console.log("n = "+k);console.log(c(k))};
test(-1);
test(0);
test(2);
test(4);
test(64);
test(96);
test(32);

Jelly, 12 bytes

»0Æf×Ṫ$-¦×2/

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How it works

»0Æf×Ṫ$-¦×2/  Main link. Argument: n

»0            Take the maximum of n and 0.
              Jelly's prime factorization does weird things for negative numbers.
  Æf          Take the prime factorization of the maximum.
        ¦     Conditional application:
    ×Ṫ$         Pop the last element of the array and and multiply all elements
                of the remaining array with it.
       -        Replace the element at index -1 with the corresponding element in
                the result.
              This effectively multiplies the last two elements of the array.
         ×2/  Multiply the factors in non-overlapping pairs. If the last element
              does not have a partner, leave it unmodified.

Haskell 150

Pretty basic answer but:

r n=p n$n-1
p 1 _=[]
p n 1=[n]
p n m
 |n`mod`m==0=p(n`div`m)(m-1)++r m
 |1>0=p n$m-1
i[x,y,z]=[x*y*z]
i(x:y:z)=x*y:i z
i _=[]
c n
 |n>0=i.r$n
 |1>0=[]

Works very straightforwardly: find all the prime factors of the input (the p function) in a way that produces them sorted ascending, and multiply them by twos (with the exception of multiplying three together if there are an odd number, to handle cases like 32 that prime factor into [2,2,2,2,2]. Example usage c 2880 = [4, 4, 4, 45].

Bonus fun

As a massively ineffecient prime generator: primes = filter (> 1) . zipWith (-) [2..] $ map (product . c) [1..].