The group was redesignated as the 343d Tactical Fighter Group and activated at Elmendorf Air Force Base, Alaska in November 1977 to serve as the headquarters for the two fighter squadrons of the 21st Composite Wing.
These were the 43d Tactical Fighter Squadron, which had been flying McDonnell F-4 Phantom IIs at Elmendorf since 1970 and the recently activated 18th Tactical Fighter Squadron, flying the Fairchild Republic A-10 Thunderbolt II.
The 21st Wing's other operational group was the 531st Aircraft Control and Warning Group, which controlled air defense units and stations throughout Alaska.
The following year aircraft maintenance was transferred from the wing and three maintenance squadrons were added to the group's strength.
The group was inactivated in January 1980.
 Its operational squadrons were reassigned directly to the 21st Wing, which converted from a composite wing to a standard fighter wing and became the 21st Tactical Fighter Wing.
 The personnel and equipment of the group's maintenance squadrons were transferred to squadrons assigned directly to the 21st Wing.
The group was redesignated as the 343d Tactical Fighter Group and activated at Elmendorf Air Force Base, Alaska in November 1977 to serve as the headquarters for the two fighter squadrons of the 21st Composite Wing. These were the 43d Tactical Fighter Squadron, which had been flying McDonnell F-4 Phantom IIs at Elmendorf since 1970 and the recently activated 18th Tactical Fighter Squadron, flying the Fairchild Republic A-10 Thunderbolt II. The 21st Wing's other operational group was the 531st Aircraft Control and Warning Group, which controlled air defense units and stations throughout Alaska. The following year aircraft maintenance was transferred from the wing and three maintenance squadrons were added to the group's strength. The group was inactivated in January 1980.  Its operational squadrons were reassigned directly to the 21st Wing, which converted from a composite wing to a standard fighter wing and became the 21st Tactical Fighter Wing.  The personnel and equipment of the group's maintenance squadrons were transferred to squadrons assigned directly to the 21st Wing.
343d Wing