This is the 570th most frequent Icelandic word.
félaginu
"The company" or "the society" (definite form of "félag").
Here, 'félaginu' refers to a formal organization, indicative from the context 'samræðunum' (the discussions).
Við tók þátt í samræðunum með félaginu.
We participated in the discussions with the society/club.
Here, 'félaginu' refers to a communal or associative group as suggested by 'meðlimur' (member).
Hann gerðist nýr meðlimur í félaginu okkar.
He became a new member of our association.
Here, 'félaginu' points to a place or established group, evident from 'heimsóttum' (visited).