From north to south in Europe there were the British 1st Army
and Canadian 1st Army (these made up the 21st Army Group, under
Montgomery); then the US 9th, 1st and 3rd Armies (these were the
12th Army Group, under US General Omar Bradley); then there were
the American 7th Army and French 1st Army (these were the 6th Army
Group, under US General Jacob Devers). All three of these Army
Groups were under Eisenhower's command.
The German attack came at the boundary between the US 9th and
1st Armies, falling more on the 1st Army. These armies became
separated when the Germans broke through. Because it looked as
though the Germans might reach a small town which was a vital
telephone line hub, which would make it difficult for Bradley to
communicate with his 9th Army Commander, and for this reason ONLY,
during the Battle the US 9th Army was placed under the direction of
Montgomery, who was himself north of the Bulge. But the 9th Army
was not really in the Ardennes Forest proper. They reformed and
faced southward along Elsenborn Ridge. to make a northern shoulder
of the Bulge, to contain the Germans and canalize them into moving
forward only on the width of their initial breakthrough.
Most of the troops actually in the Ardennes Forest were of the
US 1st Army, which was commanded by General Courtney Hodges, and
which remained in Omar Bradley's 12th Army Group, all under
Eisenhower.