I've been able to get the combinations for each hand type in holdem and 3 card to sum to the total number of combinations, but I get overwhelmed with 4 card.

Total combinations: 32C4=35960

Quads: 8
Trips with suited dangler: 896
Trips with unsuited dangler: 224
Two pair offsuit: 168
Two pair single suit:672
Two pair double suited:168
Pair no suit:2016
Pair with danglers suited: 2016
Pair with dangler suited to the pair:8064
Pair double suited: 4032
Pair with three of a suit:2016
No pair no suit:1680
No pair one suit:3360
No pair double suited:4704
No pair with three of a suit:1680
No pair with four of a suit: 280
Total: 31984

Not sure whether I'm missing categories of hands or messing up numbers (likely both).

Additionally, how would I approach finding isomorphs for this? Looked at stackexchange and it goes way over my head.

The totals for quads and two pair are correct, the others aren’t. I didn’t check subcategories. There are

8 quads
896 trips
1008 two pairs
16128 one pair
17920 no pair

8*****+1008+16128+17920 = 35960

Regarding the last part, if you are trying to make a list of strategically distinct combinations, for these starting hands it shouldn’t be too hard to go through each category. Exact ranks matter for uniqueness but exact suits don’t, only the suit pattern. For example AsAcAh2d is different from AsAcAh3d by rank and AsAcAh2s by suit pattern, but AsAcAh2s and AsAcAh2c have the same ranks and suit patterns so they’re the same.

Edit: Apparently the censor doesn’t like + 896. I’m leaving it because it’s funny.