There is only one paragraph division in Psa 136, the strong division at the conclusion to the psalm.
The elements of Psa 136 follow nearly point for point the elements of Psa 135:
Psa 136:1, Oh, give thanks to the Lord, for He is good! For His mercy endures forever.
Psa 135:3, Praise the Lord, for the Lord is good; Sing praises to His name, for it is pleasant.
Psa 136:2-3, Oh, give thanks to the God of gods + Lord of lords;
Psa 135:5, For I know that the Lord is great, and our Lord is above all gods.
Psa 136:5-9, To Him who by wisdom made the heavens + earth + sun + moon and stars.
Psa 135:6a, Whatever the Lord pleases He does (creates);
Psa 136:10, To Him who struck Egypt in their firstborn, For His mercy endures forever;
Psa 135:8, He destroyed the firstborn of Egypt, Both of man and beast.
Psa 136:11-15, And brought out Israel from among them … but overthrew Pharaoh and his army in the Red Sea;
Psa 135:9 He sent signs and wonders into the midst of you, O Egypt, Upon Pharaoh and all his servants.
Psa 136:17-20, To Him who struck down great kings + and slew famous kings + Sihon + Og—
Psa 135:10-11, He defeated many nations and slew mighty kings— Sihon + Og and all the kingdoms of Canaan—
Psa 136:21-22, And gave their land as a heritage, a heritage to Israel His servant;
Psa 135:12, And gave their land as a heritage, a heritage to Israel His people.
Psa 136:23-24, Who remembered us in our lowly state + and rescued us from our enemies;
Psa 135:14, For the Lord will judge (vindicate) His people, and He will have compassion on His servants.
I am sure this is intentional, perhaps we are seeing matching elements in a greater chiastic structure encompassing these final psalms in the book of Psalms. We will see!