CountIF question with criteria in different column

[nostradamus]

Table 1 is in spreadsheet Data, and the formulas are in the next spreadsheet
There are several Genus under Family; and several Family under Order – Hierarchical order.
(Family or Genus names are unique to each Hierarchy)

Table 1

	A	B	C	D	E
1	Order	Family	Genus	Stage	Abundance
2	Coleoptera	Elmidae	Stenelmis		5
4	Odonata	Calopterygidae	Hetaerina		1
5	Trichoptera	Hydropsychidae	Hydropsyche		67

<tbody>
</tbody>

Table 2

	A	B
1	EPT taxa abundance	73

<tbody>
</tbody>

Currently, I have this formula in col B1 (2^nd table)
=IF(SUM(SUMIF(Data!B:B,{"Ephemeroptera","Plecoptera","Trichoptera"},Data!F:F))<>0,SUM(SUMIF(Data!B:B,{"Ephemeroptera","Plecoptera","Trichoptera"},Data!F:F)),"")

The current formula gives the sum of Abundance (col E) based on the selected Orders in col A.(total= 73)
I want this formula to reflect the COUNT of Genus (col C) based on the selected Orders in col A.(= so the answer should be 3, because of 3 different Genus)

Please note, if there are repetitions of Genus, I do not want it to count it twice.
I know I can do this in a Pivot table, but I have several formulas in the 2^nd spreadsheet, and this is just one of the formulas.

Thanks.

 

[nostradamus]

Let me clarify the question a bit more.
There can be any number Orders, but the ones I'm interested are "Ephemeroptera","Plecoptera","Trichoptera"
There can also be several different Genus within Order (as in different cities within a State, only difference here is that you won't find Genus with same names under one Order, i.e., they are unique).
The info in Table (col E is irrelevant to the problem at hand, pl. disregard). I only want the COUNT of Genus, based on the Order. So in Table 1, the count for Genus would be 1, as only one of the Genus is of the desired Order (Trichoptera; in the current table, Eph. and Plec. are not present)