Statistics Advice PleaseWatch
It seems to me that you have Group 1 which is the entire sample and Groups 2 and 3 are subgroups of that sample. If groups 2 and 3 are independent you would do a independent t-test on these two groups (this describes the assumptions and shows you how to do it in SPSS). Also plot a boxplot so you can see visually whether they "look" different. This is useful reality check in case your t-test gives a surprising result which could indicate an error in your work (obviously its just an indicator, its hard to tell just by looking usually).
to decide on what tests to use you need a but more information I think. what are the three groups, how do they relate to each other and what is your independent variable (what have you taken a mean of?) as monkyvirus said if group 1 is just group 2 and 3 together then a t-test in groups 2 and 3 is fine but I'm a bit concerned as to why you want to examine it as a whole as well as together cause that may change things.