Cardinality of the smallest subgroup containing two distinct subgroups of order 2 $G$  is  a  finite  group  and  $H_1$,$H_2$  are  two  disjoint  subgroups  of  order $2$. $H$  is  the subgroup  of  smallest  order that  contains  both  $H_1$  and  $H_2.$ What  is  the  cardinality  of  $H$ $?$
$A.$ always $2$.
$B.$ always $4.$
$C.$ always $8.$
$D.$ none of the above.
Now I know , $A.$  cannot  be  as  that  would  not let them stay disjoint anymore.
$C.$  is  not  true  if  you  think  of  the  group  $K_4$ of  cardinality  $4$.
Now  problem  is  option  $B.$  Can there  be  any  such  $H$  that  has  cardinality $\neq 4$ $?$ 
What is  it  then $?$

Option $B$  won't  work . Take  this  example  :
$G=S_4$ ; $H_1=\{e,(1\ 2)\}$; $H_2=\{e,(1\ 3)\}$
