Aristophanes’ Lysistrata essay, history homework help

Read the following passage:

LYSISTRATA_x000D_
_x000D_
And not the slightest glitter of a lover!_x000D_
And since the Milesians betrayed us, I've not seen_x000D_
The image of a single upright man_x000D_
To be a marble consolation to us._x000D_
Now will you help me, if I find a means_x000D_
To stamp the war out._x000D_
_x000D_
MYRRHINE_x000D_
_x000D_
By the two Goddesses, Yes!_x000D_
I will though I've to pawn this very dress_x000D_
And drink the barter-money the same day.

-Aristophanes’ Lysistrata

Then answer the following question:

How did Greek stereotypes about gender relate to the structure of Greek society as a whole?