Do I misunderstand something?

gap> Parent(g)=Parent(hp);
true
gap> g=Parent(g);
true
gap> np:=Normalizer(g,hp);;
gap> IsNormal(np,hp);
false

================================================================

gap> g;
Group( ( 1, 7,12,16,19,21, 6)( 2, 8,13,17,20, 5,11)( 3, 9,14,18, 4,10,15),
( 1, 2)( 3, 6)( 8,15)( 9,13)(10,14)(11,12)(16,20)(17,21), ( 1,19)( 2,21)
( 3,15)( 4,20)( 5,14)( 6,13)( 7,17)(11,16)(12,18) )
gap> hp;
Subgroup( Group( ( 1, 7,12,16,19,21, 6)( 2, 8,13,17,20, 5,11)( 3, 9,14,18, 4,
 10,15), ( 1, 2)( 3, 6)( 8,15)( 9,13)(10,14)(11,12)(16,20)(17,21), ( 1,19)
( 2,21)( 3,15)( 4,20)( 5,14)( 6,13)( 7,17)(11,16)(12,18) ),
[ ( 1,15,16, 5,11,13,17)( 2,18, 4,21, 9,14, 8)( 3, 6,20,19,10, 7,12), (),
  ( 2, 9)( 3,20)( 5,11)( 7,10)( 8,14)(12,19)(13,16)(15,17)(18,21),
  ( 1, 3,21,11,12,14)( 2, 5, 6,18,15, 7)( 4,17,20, 8,13,10)( 9,16,19) ] )
gap> quit;

Peter