Child classes common method in Template Method design pattern

Question

I have to implement a solution where the code behaves differently according to different conditions.

I created some pseudocode to show it:

public void generalMethod() {

    firstMethod();
    secondMethod();
    commonMethod();
}

public void firstMethod(){
    if (condition1){
        condition1Method();
    } else {
        if (condition2){
            condition2Method();
        } else {
            defaultMethod();
        }
        condition2AndDefaultCommonMethod();
    }
}

public void secondMethod(){
    if (condition2 && condition1){
        condition1Condition2Method();
    } else if(condition2) {
        condition2Method();
    } else {
        condition1AndDefaultCommonMethod();
    }
}

I decided to use Template Method design pattern for it, because some code is common but some of them varies depending on conditions. Is it the right choice?

I created this small UML diagram for it, but I have a problem, because Condition2Template and DefaultTemplate would share a common method which is not used by Condition1Template or Condition1Condition2Template, so I don't think I should add it to the abstract class Template. Also, Condition1Template and DefaultTemplate share a common method too. Could you please advise on this?