A normal Lie subgroupoid is a wide Lie subgroupoid H ⊆ ⊆ G inside I G such that, for every h ∈ ∈ H , g ∈ ∈ G with s ( h ) = t ( h ) = s ( g ) , one has g h g − − 1 ∈ ∈ H . The isotropy groups of H are therefore normal subgroups of the isotropy groups of G .