My basils (six of them) were purchased growing very close together in a ½ quart (≈ 500 ml) pot and are at least 6 inches (ca. 15 cm) long already. They are very droopy. I think it may be difficult to separate them. Will they grow big if I just put the group in the ground as is?
6" tall and droopy sounds like insufficient light...
Spacing depends on your intended use/harvest strategy, IME.
Last year I did mine 9"x9" (23cm) with intention to harvest them younger than my usual "wait for the threat of frost" harvest date. I probably could have done 4.5x4.5 for that plan (harvest before stems got woody, not have to pick off leaves when making pesto) and as it was, I left them to the later harvest date anyway because there was not so much there earlier. This year I'll probably try 4.5x4.5 (11.5cm) and harvest at least 5 out of 9 early, letting the ones space 9x9 left go to maturity, unless I opt to chop them all - if everything doesn't go off the rails this year, anyway.
B X B X X X B X B
So plant on the B's and X's, then cut the X's young.
6 in a half-quart pot is a wee bit dense for best results in my experience.
Since this is sweet basil there is not a problem splitting them. However if you are concerned about them surviving then plant as a bunch by all means. They won't do as well as split. The reason you can split them is because basil responds well to pinching back. If you pinch back the tops by half then you have your first harvest, and you have reduced the burden on any root systems that are compromised in the splitting. Just be careful to split and keep as much root intact as possible; it won't be 100% since the roots are thin and fibrous, but in their new location (inside or outside according to environment, they are very frost tender) there is no reason you can't have 6 nice bushy plants roaring in a few weeks.
My usual way of growing basil is throwing some seed on the ground. They come up and grow no problem as a bunch a few centimetres apart. The usual seedling 6 per tray spacing should be fine straight into ground if you dont want to separate already stressed plants. Plant out in evening if daytime heat a factor and soil should be good and water in very well. Basil seeds typically just fall off mature plants to seed themselves for next season, using neither wind nor animals for dispersal. It would then seem reasonable to grow plants in fairly close proximity as per nature.
Half quart pot? 3" or less? Here is what I feel you should do. Do not plant them in the garden, as yet. I'd get good potting soil and 4" pots. Fill with potting soil and transplant your baby basils in each one. You might get a few to survive. If they are too tangled, just repot by splitting the whole bunch into two clumps, each into a 6" pot with potting soil. Keep moist but not too moist. Lots of light...have these baby basils been exposed to sunlight? Or have they been grown in a nursery, in a greenhouse, or in artificial lighting? Have they been fertilized either by the greenhouse or the nursery where you purchased them?
Send a picture of the entire gob of baby basils. Make dang sure you use potting soil and a slightly larger pot. More light but you might have to harden them off to be able to go outside into the garden. These places love to sell stuff that is going to be tough to have success so you will go buy more...more info, more pictures, please.
And when transplanting try to keep the roots and soil intact. Sure you will be breaking quite a few but DO NOT try to untangle and disturb the soil too much.