Friedrich Karl Ludwig, Duke of Schleswig-Holstein-Sonderburg-Beck
Friedrich Karl Ludwig of Schleswig- Holstein- Sonderburg- Beck( 20 August 1757 – 24 April 1816) was the ninth and penultimate Duke of Schleswig- Holstein- Sonderburg- Beck.
Friedrich Karl Ludwig was the son of Prince Karl Anton August of Schleswig- Holstein- Sonderburg- Beck and his wife Countess Charlotte of Dohna- Schlodien.
Prince Karl Anton August of Schleswig-Holstein-Sonderburg-Beck
Prince Karl Anton August of Schleswig-Holstein-Sonderburg-Beck (10 August 1727, in Marburg – 12 September 1759, in Stettin) was the son of Peter August, Duke of Schleswig-Holstein-Sonderburg-Beck and Princess Sophie of Hesse-Philippsthal.
John Adolphus, Duke of Schleswig-Holstein-Sonderburg-Plön
John Adolphus of Schleswig- Holstein- Sonderburg- Plön( or" Hans Adolf"; 8 April 1634, Ahrensbök – 2 July 1704 Ruhleben) was the second Duke of Schleswig- Holstein- Sonderburg- Plön, which had been created by a division of the Duchy of Schleswig- Holstein- Sonderburg.
August Philipp, Duke of Schleswig-Holstein-Sonderburg-Beck
August Philipp, Duke of Schleswig -Holstein- Sonderburg- Beck( 11 November 1612 – 6 May 1675) was a Danish- German prince and member of the House of Oldenburg.
After acquiring the estate of Beck in Westfalen in 1646, he took the title of Duke of Schleswig- Holstein- Sonderburg- Beck.
Peter August, Duke of Schleswig-Holstein-Sonderburg-Beck
Peter August Friedrich, Duke of Schleswig-Holstein-Sonderburg-Beck (7 December 1697 – 22 March 1775) was a Duke of Schleswig-Holstein-Sonderburg-Beck.
He was the fifth and youngest son of Frederick Louis, Duke of Schleswig-Holstein-Sonderburg-Beck and his wife Duchess Louise Charlotte of Schleswig-Holstein-Sonderburg-Augustenburg.
Born in Königsberg, Brandenburg-Prussia, Peter August became Governor General of Reval (Tallinn), Governor of Estonia, and a Field Marshal in the Russian Imperial Army.
He died in Reval.
He was only the "titular" duke, because he did not inherit the domain of Beck.
It had been inherited by his father's older brother, Duke August (1652–1689), and nephew Frederick William I (1682–1719), and was then sold by the latter's widow to Peter August's older brother, Duke Frederick William II (1687–1749), in 1732.
But he re-sold it in 1745 to Baroness Magdalena von Ledebur-Königsbrück.
Thus, by the time that Peter August became the head of this cadet branch of the Danish royal dynasty, he was "Duke of Schleswig-Holstein-Sonderburg-Beck" in name only.
He is the male line ancestor of Margrethe II of Denmark, Harald V of Norway and Charles, Prince of Wales.
Friedrich Wilhelm, Duke of Schleswig-Holstein-Sonderburg-Glücksburg
Friedrich Wilhelm, Duke of Schleswig-Holstein-Sonderburg-Glücksburg (4 January 1785 – 17 February 1831) inherited the title of Duke of Schleswig-Holstein-Sonderburg-Beck in 1816.
He subsequently changed his title to Duke of Schleswig-Holstein-Sonderburg-Glücksburg in 1825 and founded a line that includes the Royal Houses of Denmark, Greece, Norway, and the Commonwealth realms.
Louis Charles, Duke of Schleswig-Holstein-Sonderburg-Franzhagen
Louis Charles, Duke of Schleswig-Holstein-Sonderburg-Franzhagen (4 June 1684 – 11 October 1707) was a German nobleman.
He was the second son of Duke Christian Adolph of Schleswig-Holstein-Sonderburg and his wife, Duchess Eleonora Charlotte of Saxe-Lauenburg.
In 1707, he succeeded his elder brother Leopold Christian as Duke of Schleswig-Holstein-Sonderburg-Franzhagen.
However, he died later that year.
He was married to Anna Dorothea of Winterfeld.
They had two children together:
His son Christian Adolph succeeded as Duke of Schleswig-Holstein-Sonderburg-Franzhagen.
With his death in 1709, the Schleswig-Holstein-Sonderburg-Franzhagen line died out.
Frederick Louis, Duke of Schleswig-Holstein-Sonderburg-Beck
Frederick Louis of Holstein- Sonderburg- Beck( 6 April 1653 – 7 March 1728) was a Duke of Schleswig- Holstein- Sonderburg- Beck and field marshal of the Prussian Army.
He was the son of August Philipp, Duke of Schleswig- Holstein- Sonderburg- Beck and Countess Marie Sibylle of Nassau- Saarbrücken.
August, Duke of Schleswig-Holstein-Sonderburg-Beck
August, Duke of Schleswig- Holstein- Sonderburg- Beck( 13 February 1652 – 26 September 1689 in Bonn) was a German nobleman.
From 1675 until his death, he was the ruling Duke of Schleswig- Holstein- Sonderburg- Beck.
He was the second duke of this appanage.
Joachim Ernest, Duke of Schleswig-Holstein-Sonderburg-Plön
Joachim Ernest of Schleswig-Holstein- Sonderburg- Plön( 29 August 1595 – October 5, 1671), also" Joachim Ernest of Schleswig- Holstein- Plön", was the first Duke of Schleswig- Holstein- Sonderburg- Plön, which emerged from a division of the Duchy of Schleswig- Holstein- Sonderburg.

Question: Who is Prince Karl Anton August Of Schleswig-Holstein-Sonderburg-Beck's paternal grandmother?
Answer: Louise Charlotte of Schleswig-Holstein-Sonderburg-Augustenburg