Edited:Target frame.
I was referring to edgeR user guide example 3.3.1 to analyze my data which has 2 condition, 2time points and 3 genotypes,and that look like,
         Treat     Time Genotype
Sample1  Control    0h  G 1
Sample2  Control    0h  G 1
Sample3  Control    1h  G 1
Sample4  Control    1h  G 1
Sample5  Control    0h  G 2
Sample6  Control    0h  G 2
Sample7  Control    1h  G 2
Sample8  Control    1h  G 2
Sample9  Control    0h  G 3
Sample10 Control    0h  G 3
Sample11 Control    1h  G 3
Sample12 Control    1h  G 3
Sample13 Stress     0h  G 1
Sample14 Stress     0h  G 1
Sample15 Stress     1h  G 1
Sample16 Stress     1h  G 1
Sample17 Stress     0h  G 2
Sample18 Stress     0h  G 2
Sample19 Stress     1h  G 2
Sample20 Stress     1h  G 2
Sample21 Stress     0h  G 3
Sample22 Stress     0h  G 3
Sample23 Stress     1h  G 3
Sample24 Stress     1h  G 3
As additional factor "Genotype" is included, I am not sure how to make groups and contrast. I was thinking like treatment time for each treatment condition for each genotype is a group,
Group <- factor(paste(targets$Treat,targets$Time,targets$Genotype,sep="."))
In this case, how can I make contrast for identifying genes for ex,that are induced at 1hr drug treatment for only genotype "G 2"?

It's not possible to advise you unless you give the whole targets frame. From the limited rows you give, it appears that genotype is entirely confounded with treatment.
I edited original question and included full targets frame.
From this site, I understand that multiple groups cab be combined by ( group + group) / 2 format. But still I am not sure whether my steps about grouping treat, time and genotye and are correct or not.