  We investigate fairness in the allocation of indivisible items among groups
of agents using the notion of maximin share (MMS). While previous work has
shown that no nontrivial multiplicative MMS approximation can be guaranteed in
this setting for general group sizes, we demonstrate that ordinal relaxations
are much more useful. For example, we show that if $n$ agents are distributed
equally across $g$ groups, there exists a $1$-out-of-$k$ MMS allocation for $k
= O(g\log(n/g))$, while if all but a constant number of agents are in the same
group, we obtain $k = O(\log n/\log \log n)$. We also establish the tightness
of these bounds and provide non-asymptotic results for the case of two groups.
