"Die Frau" is singular (the [one] woman) while "die Männer" is plural (the [several/many] men". You may be confused because "die" is the definite article for both singular feminine nouns and plural (of any gender) nouns. In this particular case you can also tell from the nouns themselves ("Frau" is singular, while the plural form is "Frauen"; "Männer" is the plural form of "Mann") but in all cases the verb is declined differently for singular vs plural subjects -- (he/she/it) mag Katzen, (they) mögen Katzen -- so even for verbs that don't change in their plural form, the verb tells you if it's plural.
That's the standard message for when you use the wrong word.
That said, I found this on Wiktionary:
The plural Mannen is rare and poetic. It means a group of men, usually soldiers, under the command or leadership of somebody, e.g. Cäsars Mannen "Caesar's men". It is sometimes heard in sports jargon, e.g. Die Mannen von Trainer XY "Coach XY's men".