"AMDG" meaning in Latin

{
  "head_templates": [
    {
      "args": {
        "1": "la",
        "2": "phrase",
        "head": "AMDG"
      },
      "expansion": "AMDG",
      "name": "head"
    }
  ],
  "lang": "Latin",
  "lang_code": "la",
  "pos": "phrase",
  "senses": [
    {
      "alt_of": [
        {
          "extra": "for the greater glory of God",
          "word": "ad majorem Dei gloriam"
        }
      ],
      "categories": [
        {
          "kind": "other",
          "name": "Latin entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Latin links with redundant alt parameters",
          "parents": [
            "Links with redundant alt parameters",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Latin links with redundant wikilinks",
          "parents": [
            "Links with redundant wikilinks",
            "Entry maintenance"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "Initialism of ad majorem Dei gloriam (“for the greater glory of God”)."
      ],
      "id": "en-AMDG-la-phrase-jeTsQZ-~",
      "links": [
        [
          "ad majorem Dei gloriam",
          "w:ad majorem Dei gloriam"
        ]
      ],
      "tags": [
        "abbreviation",
        "alt-of",
        "initialism"
      ]
    }
  ],
  "word": "AMDG"
}

{
  "head_templates": [
    {
      "args": {
        "1": "la",
        "2": "phrase",
        "head": "AMDG"
      },
      "expansion": "AMDG",
      "name": "head"
    }
  ],
  "lang": "Latin",
  "lang_code": "la",
  "pos": "phrase",
  "senses": [
    {
      "alt_of": [
        {
          "extra": "for the greater glory of God",
          "word": "ad majorem Dei gloriam"
        }
      ],
      "categories": [
        "Latin entries with incorrect language header",
        "Latin initialisms",
        "Latin lemmas",
        "Latin links with redundant alt parameters",
        "Latin links with redundant wikilinks",
        "Latin phrases",
        "Latin terms with redundant head parameter"
      ],
      "glosses": [
        "Initialism of ad majorem Dei gloriam (“for the greater glory of God”)."
      ],
      "links": [
        [
          "ad majorem Dei gloriam",
          "w:ad majorem Dei gloriam"
        ]
      ],
      "tags": [
        "abbreviation",
        "alt-of",
        "initialism"
      ]
    }
  ],
  "word": "AMDG"
}