Question: Who is the paternal grandmother of Prince Max, Duke In Bavaria?

Duke Franz Joseph in Bavaria
Duke Franz Joseph in Bavaria, full German name:" Franz Joseph Michael Karl
Maria Evaristus Quirinus Ottokar Herzog in Bayern"( 23 March 1888, Schloss Tegernsee, Kingdom of Bavaria – 23 September 1912, Munich, Kingdom of Bavaria) was a Duke in Bavaria and member of the House of Wittelsbach.
Franz Joseph was the fifth and youngest child of Duke Karl- Theodor in Bavaria and his wife Infanta Maria Josepha of Portugal.
Franz Joseph was the brother of Duke Ludwig Wilhelm in Bavaria and sisters Duchess Amalie in Bavaria, Duchess Sophie Adelheid in Bavaria, Duchess Elisabeth in Bavaria and Duchess Marie Gabrielle in Bavaria.
Tjuyu
Tjuyu( sometimes transliterated as Thuya or Thuyu) was an Egyptian noblewoman and the mother of queen Tiye, and the wife of Yuya.
She is the grandmother of Akhenaten, and great grandmother of Tutankhamun.
Kaoru Hatoyama
After the elections of 2009, she became more widely known as the grandmother of Prime Minister Yukio Hatoyama and his politician brother Kunio Hatoyama.
Hubba bint Hulail
Hubba bint Hulail was the grandmother of Hashim ibn' Abd Manaf, thus the great- great- great- grandmother of the Islamic" Nabī"( Prophet) Muhammad ibn Abdullah.
Albrecht, Duke of Bavaria
Albrecht, Duke of Bavaria (Albrecht Luitpold Ferdinand Michael; 3 May 1905 – 8 July 1996) was the son of the last crown prince of Bavaria, Rupprecht, and his first wife, Duchess Marie Gabrielle in Bavaria.
He was the only child from that marriage that reached adulthood.
His paternal grandfather was Ludwig III of Bavaria, the last king of Bavaria, who was deposed in 1918.
Hannah Arnold
Hannah Arnold, also known as Hannah Waterman King, was the grandmother of Benedict Arnolds children.
Duke Siegfried August in Bavaria
Duke Siegfried in Bavaria, full German name:" Siegfried August Maximilian Maria, Herzog in Bayern"( 10 July 1876, Bamberg, Kingdom of Bavaria – 12 March 1952, Munich, Republik of Bavaria) was a Duke in Bavaria and member of the House of Wittelsbach.
Siegfried August was the first of three sons of Duke Maximilian Emanuel in Bavaria and his wife Princess Amalie of Saxe- Coburg and Gotha.
Siegfried August was the brother of" Christoph" Joseph Clemens Maria, Duke in Bavaria and" Luitpold" Emanuel Ludwig Maria, Duke in Bavaria.
Prince Max, Duke in Bavaria
Max-Emanuel Ludwig Maria Herzog in Bayern (sometimes styled Prince Max of Bavaria, Duke in Bavaria; born 21 January 1937) as the younger son of Albrecht, Duke of Bavaria, is the heir presumptive to both the headship of the former Bavarian royal house and the Jacobite succession.
He was born a Prince of Bavaria, as a member of the royal line of the House of Wittelsbach, but has been using the title "Herzog in Bayern" or Duke in Bavaria, since he was adopted as an adult by his great-uncle, Duke Ludwig Wilhelm in Bavaria, the last bearer of that title of a junior branch of the House of Wittelsbach, from whom he inherited considerable estates at Tegernsee Abbey (including a brewery), Banz Abbey and Kreuth.
Gisela, Margravine of Meissen
Princess" Gisela"
Maria Karolina Adelgunde of Bavaria( Full German name:" Gisela Maria Karolina Adelgunde, Prinzessin von Bayern")( born 10 September 1964 at Schloss Leutstetten near Starnberg, Bavaria, Germany) is a Princess of Bavaria and member of the House of Wittelsbach by birth and a Princess of Saxe- Gessaphe and member of the House of Saxe- Gessaphe by marriage.
Gisela is the seventh and youngest child of Prince Rasso of Bavaria and his wife Archduchess Theresa of Austria.
Through her father, Gisela is a great- granddaughter of Ludwig III, the last sovereign of the Kingdom of Bavaria.
She is a cousin of Prince Luiz of Orléans- Braganza, Prince Bertrand of Orléans- Braganza, Prince Eudes of Orléans- Braganza, Eleanora, Princess of Ligne.
She is also a second cousin of Prince Max, Duke in Bavaria and Princess Maria Isabella of Savoy- Genoa.
She is also a fourth cousin of Carl, Duke of Württemberg.
She is a fifth cousin of Karl von Habsburg and Prince Lorenz of Belgium, Archduke of Austria- Este.
Through her marriage, she is the Margravine of Meissen.
Princess Gisela was a guest at the 2011 wedding of Prince Georg Friedrich of Prussia and Princess Sophie of Isenburg.
Princess Elisabeth, Duchess in Bavaria
Princess Elisabeth, Duchess in Bavaria( born 31 December 1940) is the wife of Prince Max, Duke in Bavaria, heir presumptive to both the former Bavarian Royal House and the Jacobite Succession.

Answer: Duchess Marie Gabrielle in Bavaria