Qabisah bin Dhu'ayb (may Allah have mercy on him) said that Sayyiduna Umar (may Allah be pleased with him) ruled that the grandfather shares with the full brothers and the paternal brothers as long as sharing is better for him than a third of the wealth. If the brothers are many, the grandfather is given a third and the remainder goes to the brothers according to "For the male, the like of the share of two females" [Surah al-Nisa: 11]. He also ruled that the full siblings, male and female, are more entitled than the paternal siblings, except that the paternal brothers are counted with the full siblings in sharing against the grandfather, and (their portion) is then returned to the full siblings.
The paternal siblings get nothing alongside the full siblings, except that the paternal brothers are counted for the benefit of the full sisters. If anything remains after the full sisters are given their shares, it goes to the paternal brothers according to "For the male, the like of the share of two females" [Surah al-Nisa: 11].
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الفرائض / 12432