Rewrite the title as: SQL grouping of columns using reversed values

Question

Suppose I have a table like this:

+---+---+---+---+---+
|G1 |G2 |G3 |G4 | V |
+---+---+---+---+---+
| A | B | C | D | 2 |
| E | F | G | H | 4 |
| C | D | A | B | 2 |
| E | F | G | H | 3 |
| E | I | G | L | 7 |
+---+---+---+---+---+

G1 and G3 are VARCHAR types, G2 and G4 are INT types

If I do a simple GROUP BY on G1..G4, I get:

SELECT G1,G2,G3,G4,SUM(V) as V FROM Table GROUP BY G1, G2, G3, G4;

    +---+---+---+---+---+
    |G1 |G2 |G3 |G4 | V |
    +---+---+---+---+---+
    | A | B | C | D | 2 |
    | E | F | G | H | 7 |
    | C | D | A | B | 2 |
    | E | I | G | L | 7 |
    +---+---+---+---+---+

I want to know if it is possible to do aggregation on inverted values ​​G1, G2 <-> G3, G4. The result I want is this:

+---+---+---+---+---+      +---+---+---+---+---+
|G1 |G2 |G3 |G4 | V |      |G1 |G2 |G3 |G4 | V |
+---+---+---+---+---+      +---+---+---+---+---+
| A | B | C | D | 4 |  或  | C | D | A | B | 4 |
| E | F | G | H | 7 |      | E | F | G | H | 7 |
| E | I | G | L | 7 |      | E | I | G | L | 7 |
+---+---+---+---+---+      +---+---+---+---+---+

I tried getting the reversed rows but I still can't aggregate on them due to duplicates. My test query is:

SELECT DISTINCT *
FROM Table t1
JOIN Table t2 on t1.G1 = t2.G3 and t1.G2=t2.G4 and t1.G3=t2.G1 and t1.G4=t2.G2

    +---+---+---+---+---+---+---+---+---+---+
    |G1 |G2 |G3 |G4 | V |G1 |G2 |G3 |G4 | V |
    +---+---+---+---+---+---+---+---+---+---+
    | A | B | C | D | 2 | C | D | A | B | 2 |
    | C | D | A | B | 2 | A | B | C | D | 2 |
    +---+---+---+---+---+---+---+---+---+---+

Answer 1

If I understand correctly, reverse the order of the columns so that A B C D corresponds to C D A B.

select 
         case when(g1 > g3) then g3 else g1 end G1,
         case when(g1 > g3) then g4 else g2 end G2,
         case when(g1 > g3) then g1 else g3 end G3,
         case when(g1 > g3) then g2 else g4 end G4, sum(V)
from tbl
group by case when(g1 > g3) then g3 else g1 end,
         case when(g1 > g3) then g4 else g2 end,
         case when(g1 > g3) then g1 else g3 end,
         case when(g1 > g3) then g2 else g4 end

db<>fiddle