Elasticsearch aggregations with filter match

I have a document with a collection of nested documents:

{
  "_source": {
    ...
    "groups": [
      {
        "group_id": 100,
        "parent_group_id": 1,
        "title": "Wheel",
        "parent_group_title": "Parts"
      },
      {
        "group_id": 200,
        "parent_group_id": 2,
        "title": "Seat",
        "parent_group_title": "Parts"
      }
    ]
    ...
  }
}

Mapping looks the next:

{
  ...,

  "groups": {
    "type": "nested",
    "properties": {
      "group_id": {
        "type": "long"
      },
      "title": {
        "type": "text",
        "analyzer": "my_custom_analyzer",
        "term_vector": "with_positions_offsets",
        "fields": {
          "keyword": {
            "type": "keyword"
          }
        }
      },
      "parent_group_id": {
        "type": "long"
      },
      "parent_group_title": {
        "type": "text",
        "analyzer": "my_custom_analyzer",
        "term_vector": "with_positions_offsets",
        "fields": {
          "keyword": {
            "type": "keyword"
          }
        }
      }
    }
  },

  ...
}

What I'm trying to do is the next aggregation:

{
  "query": {
    "bool": {
      "must": [
        {
          "nested": {
            "path": "groups",
            "query": {
              "match": {
                "groups.title": {
                  "query": "whe"
                }
              }
            }
          }
        }
      ]
    }
  },
  "size": 0,
  "aggs": {
    "filtered": {
      "filter": {
        "bool": {
          "must": [
            {
              "nested": {
                "path": "groups",
                "query": {
                  "match": {
                    "groups.title": {
                      "query": "whe"
                    }
                  }
                }
              }
            }
          ]
        }
      },
      "aggs": {
        "groups": {
          "nested": {
            "path": "groups"
          },
          "aggs": {
            "titles": {
              "terms": {
                "field": "groups.title.keyword",
                "size": 5
              },
              "aggs": {
                "parents": {
                  "terms": {
                    "field": "groups.parent_group_title.keyword",
                    "size": 3
                  }
                }
              }
            }
          }
        }
      }
    }
  }
}

With such query I'm getting results something like the next:

  "aggregations" : {
    "filtered" : {
      "doc_count" : ...,
      "groups" : {
        "doc_count" : ...,
        "titles" : {
          "doc_count_error_upper_bound" : ...,
          "sum_other_doc_count" : ...,
          "buckets" : [
            {
              "key" : "Seat",
              "doc_count" : 10,
              "parents" : {
                "doc_count_error_upper_bound" : 0,
                "sum_other_doc_count" : 10,
                "buckets" : [
                  {
                    "key" : "Parts",
                    "doc_count" : 6
                  },
                  {
                    "key" : "Other",
                    "doc_count" : 4
                  }
                ]
              }
            },
            {
              "key" : "Wheel",
              "doc_count" : 3,
              "parents" : {
                "doc_count_error_upper_bound" : 0,
                "sum_other_doc_count" : 3,
                "buckets" : [
                  {
                    "key" : "Parts",
                    "doc_count" : 2
                  },
                  {
                    "key" : "Other",
                    "doc_count" : 1
                  }
                ]
              }
            }
          ]
        }
      }
    }
  }

But what I want is that only result with key Wheel is to appear in the result buckets (or any other results matching to whe search string).

Hope the question is clear enough. What I'm doing wrong? Any suggestings or changing data structure or query?

UPD:
Adding a my_custom_analyzer for reference:

{
  "my_custom_analyzer": {
    "type": "custom",
    "tokenizer": "ngram",
    "filter": [
      "lowercase",
      "asciifolding"
    ],
    "char_filter": [
      "html_strip"
    ],
    "min_gram": 2,
    "max_gram": 15,
    "token_chars": [
      "letter",
      "digit"
    ]
  }
}