England will have to face Australia in the Glasgow Games while Wales will face South Pacific nations Samoa and Papua New Guinea, as well as Malaysia, in their group.
The All Blacks have won all four Commonwealth gold medals so far and will also take on Nigeria and Canada in their group.
England face Sri Lanka and Uganda in their pool games.
Sixteen teams take part in the tournament, including South Africa, which will be held at Ibrox Stadium on July 26-27.
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