expression manipulation - Group symbols by a given partition of the occuring symbols

I have following expression

$$-3 b_{\sigma _d}-3 b_{\sigma _v}-b-b_2+2 j-2 j_2-2 j_3+2 j_6+12$$

Mathematica input

12-b+2 j-Subscript[b, 2]-3 Subscript[b, Subscript[\[Sigma], d]]-3 Subscript[b, Subscript[\[Sigma], v]]-2 Subscript[j, 2]-2 Subscript[j, 3]+2 Subscript[j, 6]

I want to reorder this expression by partitioning the occuring symbols. Additionally, common factors of the partitions should be factored out:

Partition (given by user): $$\{\{j,j_2,j_3,j_6\},\{b,b_2,b_{\sigma_d},b_{\sigma _v}\}\}$$

The order should also be respected. The end result would look like $$2(j-j_2-j_3+j_6)-(b+b_2+3 b_{\sigma _d}+3 b_{\sigma _v})+12$$

I have considered FactorTerms[poly,{x_1,x_2,...] and Collect[expr,{x_1,x_2,...}] but was not successful to achieve this.

Answer

expr = 12 - b + 2 j - Subscript[b, 2] - 
 3 Subscript[b, Subscript[σ, d]] - 

 3 Subscript[b, Subscript[σ, v]] - 2 Subscript[j, 2] - 
 2 Subscript[j, 3] + 2 Subscript[j, 6]

Inactive[Plus] @@ 
  (Total /@ Join @@ 
     GatherBy[List @@ expr, MatchQ[_ (# | Subscript[#, _])] & /@ {j, b}])

TeXForm @ %

$\Large 12+\left(-3 b_{\sigma _d}-3 b_{\sigma _v}-b-b_2\right)+\left(2 j-2 j_2-2 j_3+2 j_6\right)$

Update:

ClearAll[f]
f[e_] := Row @ Flatten @ Append[Reverse @ Values @ 
   GroupBy[Transpose[{Coefficient[e, #], #}& @ Variables[e]] /.
      {a_, b_Symbol} :> {a, Subscript[b, 0]}, #[[2,1]]&, 
     Row[{# /. { 1 -> " + ", -1 -> " - "}, "(", HoldForm @ #2, ")"}]& @@ 
     FactorList[ Dot @@ Transpose[#]][[All, 1]]&],
      If[# < 0, {" - ", -#}, {" + ", #}]&[e /.

       (Alternatives@@Variables[e] -> 0)] /. {_, 0} -> Nothing] /.
    Subscript[a_, 0] -> a

Examples:

f @ expr 

System`Convert`CommonDump`templateBoxToDisplay = BoxForm`TemplateBoxToDisplayBoxes;

TeXForm @ f @ expr

$\Large 2(j-j_2-j_3+j_6)\text{ - }(b+b_2+3 b_{\sigma _d}+3 b_{\sigma _v})\text{ + }12$

f[- expr - 20] // TeXForm

$\Large -2(j-j_2-j_3+j_6)\text{ + }(b+b_2+3 b_{\sigma _d}+3 b_{\sigma _v})\text{ - }32$

Note: I used Carl's answer from this q/a to make TeXForm process Rows properly.