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SELECT 
  f.feature_id, 
  f.purpose, 
  p.product_id, 
  p.parent_product_id, 
  g.id, 
  g.code 
FROM 
  cscart_product_variation_group_features AS f 
  INNER JOIN cscart_product_variation_groups AS g ON f.group_id = g.id 
  INNER JOIN cscart_product_variation_group_products AS p ON f.group_id = p.group_id 
WHERE 
  p.product_id IN (337, 341, 346)

Query time 0.00047

Explain
id	select_type	table	type	possible_keys	key	key_len	ref	rows	Extra
1	SIMPLE	p	range	PRIMARY,idx_group_id	PRIMARY	3		3	Using index condition
1	SIMPLE	g	eq_ref	PRIMARY	PRIMARY	3	cscart_dev_4_16.p.group_id	1
1	SIMPLE	f	ALL	idx_group_id				6	Using where; Using join buffer (flat, BNL join)

Result

feature_id	purpose	product_id	parent_product_id	id	code
549	group_catalog_item	337	1	13	PV-9318A163F
549	group_catalog_item	341	0	13	PV-9318A163F
549	group_catalog_item	346	0	13	PV-9318A163F
548	group_variation_catalog_item	337	1	13	PV-9318A163F
548	group_variation_catalog_item	341	0	13	PV-9318A163F
548	group_variation_catalog_item	346	0	13	PV-9318A163F