Then what is the problem? You can check with the ID of the button.
Try this:
protected void buttonGroup_Click(object sender, EventArgs e)
{
Button btn = (Button)sender;
if(btn.ID == "Button1")
TextBox1.Text = "Button1 clicked";
else if(btn.ID == "Button2")
TextBox1.Text = "Button2 clicked";
else if(btn.ID == "Button3")
TextBox1.Text = "Button3 clicked";
}
Hope it helps.!
--Amit