Java 8 is not maintaining the order while grouping

Not maintaining the order is a property of the Map that stores the result. If you need a specific Map behavior, you need to request a particular Map implementation. E.g. LinkedHashMap maintains the insertion order:

groupedResult = people.collect(Collectors.groupingBy(
    p -> new GroupingKey(p, groupByColumns),
    LinkedHashMap::new,
    Collectors.mapping((Map<String, Object> p) -> p, toList())));

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By the way, there is no reason to copy the contents of mapList into an array before creating the Stream. You may simply call mapList.stream() to get an appropriate Stream.

Further, Collectors.mapping((Map<String, Object> p) -> p, toList()) is obsolete. p->p is an identity mapping, so there’s no reason to request mapping at all:

groupedResult = mapList.stream().collect(Collectors.groupingBy(
    p -> new GroupingKey(p, groupByColumns), LinkedHashMap::new, toList()));

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But even the GroupingKey is obsolete. It basically wraps a List of values, so you could just use a List as key in the first place. Lists implement hashCode and equals appropriately (but you must not modify these key Lists afterwards).

Map<List<Object>, List<Object>> groupedResult=
  mapList.stream().collect(Collectors.groupingBy(
    p -> groupByColumns.stream().map(p::get).collect(toList()),
    LinkedHashMap::new, toList()));

Based on @Holger's great answer. I post this to help those who want to keep the order after grouping as well as changing the mapping.

Let's simplify and suppose we have a list of persons (int age, String name, String adresss...etc) and we want the names grouped by age while keeping ages in order:

final LinkedHashMap<Integer, List<String> map = myList
                .stream()
                .sorted(Comparator.comparing(p -> p.getAge())) //sort list by ages
                .collect(Collectors.groupingBy(p -> p.getAge()),
                        LinkedHashMap::new, //keeps the order
                        Collectors.mapping(p -> p.getName(), //map name
                                Collectors.toList())));