my %GROUPS => (
    A => 1,
    B => 2,
    C => 3
);


my %FOO = (
    A => {
        1 => x,
        2 => y,
        3 => z
    },
    B => {
        1 => x,
        2 => y,
        3 => z
    },
);

for my $group (keys %GROUPS) {
    my $foo = $FOO{$group};

    for (keys %$foo) {
        print("$_ in group $group: $foo->{$_}\n");
    }
}
[download]

But why does %GROUPS have values that aren't used? You probably want:

my %GROUPS => (
    A => {
        1 => x,
        2 => y,
        3 => z
    },
    B => {
        1 => x,
        2 => y,
        3 => z
    },
);

for my $group (keys %GROUPS) {
    my $foo = $GROUPS{$group};

    for (keys %$foo) {
        print("$_ in group $group: $foo->{$_}\n");
    }
}
[download]