Order by Object key in ng-repeat

An option would be use an intermediate filter.

PLUNK AND Code Snippet

var app = angular.module('app', []);

app.controller('MainCtrl', function($scope) {
  
  $scope.template = {
    "0": { data: "ZERO" },
    "1": { data: "ONE" },
    "2": { data: "TWO"  },
    "3": { data: "TREE" },
    "5": { data: "FIVE" },
    "6": { data: "SIX" },
    "10":{ data:  "TEN" },
    "11": { data: "ELEVEN" },
    "12": { data: "TWELVE" },
    "13": { data: "THIRTEEN" },
    "20": { data: "TWENTY"}
  }
 
});

app.filter('toArray', function() { return function(obj) {
    if (!(obj instanceof Object)) return obj;
    return _.map(obj, function(val, key) {
        return Object.defineProperty(val, '$key', {__proto__: null, value: key});
    });
}});
<script src="https://ajax.googleapis.com/ajax/libs/angularjs/1.2.23/angular.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/underscore.js/1.7.0/underscore.js"></script>

<body ng-app="app" ng-controller="MainCtrl">
    <div ng-repeat="(key, value) in template| toArray | orderBy:key">{{key}} : {{value.$key}} : {{value.data}}</div>
<body>

NOTE:

The above filter requires Underscore.js, if you don’t use it, can rewrite the filter.

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