Louis VI, Landgrave of Hesse-Darmstadt
Louis VI of Hesse-Darmstadt  (25 January 1630 – 24 April 1678) was Landgrave of Hesse-Darmstadt from 1661 to 1678.
He was the eldest of three sons of the Landgrave George II of Hesse-Darmstadt and Sophia Eleonore of Saxony.
Philip of Hesse-Darmstadt
Philip of Hesse- Darmstadt( July 20, 1671 in Darmstadt – August 11, 1736 in Vienna) was a Prince of Hesse- Darmstadt, Imperial Field marshal and Governor of Mantua.
Ernest Louis, Landgrave of Hesse-Darmstadt
Ernest Louis of Hesse-Darmstadt  (15 December 1667 – 12 September 1739) was Landgrave of Hesse-Darmstadt from 1678 to 1739.
His parents were Landgrave Louis VI of Hesse-Darmstadt and Elisabeth Dorothea of Saxe-Gotha-Altenburg (1640–1709).
Ernest Louis's desire to emulate the French court under Louis XIV ran his country into debt.
Among those patronized in this cultural milieu were the Baroque composer Christoph Graupner and the gambist Ernst Christian Hesse; also bringing into his service architect Louis Remy de la Fosse for his extensive building program.
Upon his death in 1739, his country's debt was 4 million "gulden", ten times the annual revenue.
Marie Hedwig of Hesse-Darmstadt
Marie Hedwig of Hesse- Darmstadt( 26 November 1647 in Giessen – 19 April 1680 in Ichtershausen) was a landgravine of Hesse- Darmstadt by birth and by marriage Duchess of Saxe- Meiningen.
Sophia Eleonore of Hesse-Darmstadt
Sophia Eleonore of Hesse- Darmstadt( 7 January 1634 in Darmstadt – 7 October 1663 in Bingenheim, now part of Echzell), was Landgravine of Hesse- Darmstadt by birth and by marriage Landgravine of Hesse- Homburg.
She was a daughter of Landgrave George II of Hesse- Darmstadt( 1605 – 1661) from his marriage to Sophia Eleonore( 1609 – 1671), the daughter of Elector John George I of Saxony.
Prince Charles William of Hesse-Darmstadt
Karl Wilhelm of Hesse- Darmstadt( 17 June 1693, Nidda- 17 May 1707, Gießen) was a Prince of Hesse- Darmstadt.
Prince George Charles of Hesse-Darmstadt
George Charles( German:" Georg Karl") of Hesse- Darmstadt( 14 June 1754- 28 January 1830, Schüttrisberg, now in Slovakia) was a German prince of the House of Hesse- Darmstadt.
He was the fourth child and third son of Prince George William of Hesse- Darmstadt and Countess Maria Louise Albertine of Leiningen- Dagsburg- Falkenburg.
Louis V, Landgrave of Hesse-Darmstadt
Louis V of Hesse-Darmstadt (24 September 1577 – 27 July 1626) was the Landgrave of Hesse-Darmstadt from 1596 to 1626.
He was born on 24 September 1577 as the son of George I, Landgrave of Hesse-Darmstadt and Magdalene of Lippe.
In 1604 he inherited a part of Hessen-Marburg after the death of Louis IV of Hesse-Marburg who was childless.
The other half went to Maurice of Hesse-Kassel (or Hesse-Cassel), but since Maurice was a Calvinist, Ludwig claimed a right on the whole of Hesse-Marburg.
Lutheran professors of the University of Marburg who refused to convert to Calvinism founded in 1607 the University of Gießen which was named "Ludoviciana".
This led to a conflict during the Thirty Years' War, between Louis V, who stood on the side of the Emperor, and Maurice, who was on the side of the Protestants.
Hesse-Darmstadt suffered severely from the ravages from the Swedes during the conflict.
The Landgrave died in 1626 and he was succeeded by George II, Landgrave of Hesse-Darmstadt.
In 1722, Johann Georg Liebknecht, an astronomer at the University of Gießen, named a star, which he thought was a planet, Sidus Ludoviciana after Ludwig V.
Prince Francis Ernest of Hesse-Darmstadt
Francis Ernest of Hesse-Darmstadt (born 25 January 1695 in Gießen; died: 8 January 1716 in Darmstadt) was a German nobleman.
He was the third son of Count Landgrave Ernest Louis of Hesse-Darmstadt (1667–1739) from his marriage to Dorothea Charlotte (1661–1705), daughter of the Margrave Albert of Brandenburg-Ansbach.
He replaced his brother Charles William of Hesse-Darmstadt as Colonel of the Hesse-Darmstadt Kreis Regiment when Charles William died during the War of Spanish Succession.
Landgravine Elisabeth Amalie of Hesse-Darmstadt
Landgravine Elisabeth Amalie of Hesse-Darmstadt (Elisabeth Amalie Magdalene; 20 March 1635 – 4 August 1709) was a princess of Hesse-Darmstadt and wife of the Prince-elector of the Palatinate.

Question: Who is the paternal grandmother of Prince Francis Ernest Of Hesse-Darmstadt?
Answer: Elisabeth Dorothea of Saxe-Gotha-Altenburg