"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"
        },
        {
          "kind": "other",
          "name": "Pages with 1 entry",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Pages with entries",
          "parents": [],
          "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",
        "Pages with 1 entry",
        "Pages with entries"
      ],
      "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"
}