(a) If a beneficiary is not designated, or if the estate is the beneficiary and the estate would not be probated if no amount were due from this system, all of the amount due by reason of the death of a member or retired member, including retirement allowances accrued but not received prior to death, shall be paid directly without probate to the surviving next of kin of the deceased, or the guardians of such survivors’ estates, share and share alike.
(b) Such payment shall be made in the same order in which the following groups are listed:
(1) Spouse.
(2) Children.
(3) Father and mother.
(4) Grandchildren.
(5) Brothers and sisters.
(6) Nieces and nephews.