In all other groups, there is a gap of one letters as in the alphabet between first and third letters.

All others have only one vowel.

All except '18' are square of natural numbers.
(5)² = 25, (3)² = 9, (4)² = 16

4867 ? 4 + 8 + 6 + 7 = 25, which is divisible by 5.
5555 ? 5 + 5 + 5 + 5 = 20, which is divisible by 5.
6243 ? 6 + 2 + 4 + 3 = 15, which is divisible by 5.
6655 ? 6 + 6 + 5 + 5 = 22, which is not divisible by 5.

All others are complete squares.

All others are prime numbers.

All others are prime numbers.

All others are divisible by 3.

All others have only 3 factors.
12 = 2 x 2 x 3, 28 = 2 x 2 x 7, 52 = 2 x 2 x 13
68 = 2 x 2 x 17, 96 = 2 x 2 x 2 x 2 x 2 x 3

All others have only 2 factors with prime number.
26 = 2 x 13, 34 = 2 x 17, 72 = 2 x 2 x 2 x 3 x 3,
46 = 2 x 23, 38 = 2 x 19