The most common and most likely answer to this crossword clue is the 6 letter word FAMILY
F
A
M
I
L
Y
Buddy explains!

The straight part
We know that "group" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case group = family.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does FAMILY mean?
FAMILY noun- A group of people who are closely related to one another (by blood, marriage or adoption); kin; for example, a set of parents and their children; an immediate family.
- An extended family; a group of people who are related to one another by blood or marriage.
- A (close-knit) group of people related by blood, friendship, marriage, law, or custom, especially if they live or work together.
- Lineage, especially an honorable one
- A rank in the classification of organisms, below order and above genus; a taxon at that rank.
- Any group or aggregation of things classed together as kindred or related from possessing in common characteristics which distinguish them from other things of the same order.
- A group of instruments having the same basic method of tone production.
- A group of languages believed to have descended from the same ancestral language.
- Used attributively.
- Suitable for children and adults.
- Conservative, traditional.
- Homosexual.
- A person belonging to a particular family; a close relative or relation.