diff --git a/moto/iam/models.py b/moto/iam/models.py
index a7e58428..0f0f4c05 100644
--- a/moto/iam/models.py
+++ b/moto/iam/models.py
@@ -82,6 +82,10 @@ class ManagedPolicy(Policy):
         self.attachment_count -= 1
         del role.managed_policies[self.name]
 
+    def attach_to_group(self, group):
+        self.attachment_count += 1
+        group.managed_policies[self.name] = self
+
     def attach_to_user(self, user):
         self.attachment_count += 1
         user.managed_policies[self.name] = self
@@ -249,6 +253,7 @@ class Group(BaseModel):
         )
 
         self.users = []
+        self.managed_policies = {}
         self.policies = {}
 
     def get_cfn_attribute(self, attribute_name):
@@ -433,14 +438,36 @@ class IAMBackend(BaseBackend):
         except KeyError:
             raise IAMNotFoundException("Policy {0} was not found.".format(policy_arn))
 
+    def attach_group_policy(self, policy_arn, group_name):
+        arns = dict((p.arn, p) for p in self.managed_policies.values())
+        try:
+            policy = arns[policy_arn]
+        except KeyError:
+            raise IAMNotFoundException("Policy {0} was not found.".format(policy_arn))
+        policy.attach_to_group(self.get_group(group_name))
+
+    def detach_group_policy(self, policy_arn, group_name):
+        arns = dict((p.arn, p) for p in self.managed_policies.values())
+        try:
+            policy = arns[policy_arn]
+        except KeyError:
+            raise IAMNotFoundException("Policy {0} was not found.".format(policy_arn))
+        policy.detach_from_group(self.get_group(group_name))
+
     def attach_user_policy(self, policy_arn, user_name):
         arns = dict((p.arn, p) for p in self.managed_policies.values())
-        policy = arns[policy_arn]
+        try:
+            policy = arns[policy_arn]
+        except KeyError:
+            raise IAMNotFoundException("Policy {0} was not found.".format(policy_arn))
         policy.attach_to_user(self.get_user(user_name))
 
     def detach_user_policy(self, policy_arn, user_name):
         arns = dict((p.arn, p) for p in self.managed_policies.values())
-        policy = arns[policy_arn]
+        try:
+            policy = arns[policy_arn]
+        except KeyError:
+            raise IAMNotFoundException("Policy {0} was not found.".format(policy_arn))
         policy.detach_from_user(self.get_user(user_name))
 
     def create_policy(self, description, path, policy_document, policy_name):
@@ -458,39 +485,15 @@ class IAMBackend(BaseBackend):
 
     def list_attached_role_policies(self, role_name, marker=None, max_items=100, path_prefix='/'):
         policies = self.get_role(role_name).managed_policies.values()
+        return self._filter_attached_policies(policies, marker, max_items, path_prefix)
 
-        if path_prefix:
-            policies = [p for p in policies if p.path.startswith(path_prefix)]
-
-        policies = sorted(policies, key=lambda policy: policy.name)
-        start_idx = int(marker) if marker else 0
-
-        policies = policies[start_idx:start_idx + max_items]
-
-        if len(policies) < max_items:
-            marker = None
-        else:
-            marker = str(start_idx + max_items)
-
-        return policies, marker
+    def list_attached_group_policies(self, group_name, marker=None, max_items=100, path_prefix='/'):
+        policies = self.get_group(group_name).managed_policies.values()
+        return self._filter_attached_policies(policies, marker, max_items, path_prefix)
 
     def list_attached_user_policies(self, user_name, marker=None, max_items=100, path_prefix='/'):
         policies = self.get_user(user_name).managed_policies.values()
-
-        if path_prefix:
-            policies = [p for p in policies if p.path.startswith(path_prefix)]
-
-        policies = sorted(policies, key=lambda policy: policy.name)
-        start_idx = int(marker) if marker else 0
-
-        policies = policies[start_idx:start_idx + max_items]
-
-        if len(policies) < max_items:
-            marker = None
-        else:
-            marker = str(start_idx + max_items)
-
-        return policies, marker
+        return self._filter_attached_policies(policies, marker, max_items, path_prefix)
 
     def list_policies(self, marker, max_items, only_attached, path_prefix, scope):
         policies = self.managed_policies.values()
@@ -504,6 +507,9 @@ class IAMBackend(BaseBackend):
             policies = [p for p in policies if not isinstance(
                 p, AWSManagedPolicy)]
 
+        return self._filter_attached_policies(policies, marker, max_items, path_prefix)
+
+    def _filter_attached_policies(self, policies, marker, max_items, path_prefix):
         if path_prefix:
             policies = [p for p in policies if p.path.startswith(path_prefix)]