Label	Element	Value
APIC, Share-Based Payment Arrangement, Increase for Cost Recognition	us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue	$ 49,895,000
Stock Issued During Period, Value, Noncontrolling Interest, Increase from Business Combination	stgw_StockIssuedDuringPeriodValueNoncontrollingInterestIncreaseFromBusinessCombination	778,658,000
Contribution from Limited Liability Company (LLC)	stgw_ContributionFromLimitedLiabilityCompanyLLC	11,834,000
Noncontrolling Interest, Decrease from Distributions to Noncontrolling Interest Holders	us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders	934,000
Noncontrolling Interest, Decrease from Distributions to Noncontrolling Interest Holders	us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders	7,561,000
Stock Repurchased and Retired During Period, Value	us-gaap_StockRepurchasedAndRetiredDuringPeriodValue	820,000
Stockholders' Equity, Other	us-gaap_StockholdersEquityOther	161,000
Stockholders' Equity, Other	us-gaap_StockholdersEquityOther	55,000
Stockholders' Equity, Other	us-gaap_StockholdersEquityOther	(300,000)
Net Income (Loss) Attributable to Parent, Equity Statement Impact	stgw_NetIncomeLossAttributableToParentEquityStatementImpact	3,102,000
Net Income (Loss) Attributable to Parent, Equity Statement Impact	stgw_NetIncomeLossAttributableToParentEquityStatementImpact	2,229,000
Net Income (Loss) Attributable to Parent, Equity Statement Impact	stgw_NetIncomeLossAttributableToParentEquityStatementImpact	27,435,000
Retained Earnings [Member]
Net Income (Loss), Including Noncontrolling Interests, Equity Statement Impact	stgw_NetIncomeLossIncludingNoncontrollingInterestsEquityStatementImpact	(4,545,000)
Redeemable noncontrolling interest, changes in redemption value	stgw_Redeemablenoncontrollinginterestchangesinredemptionvalue	(1,608,000)
Parent [Member]
APIC, Share-Based Payment Arrangement, Increase for Cost Recognition	us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue	49,895,000
Stock Issued During Period, Value, Noncontrolling Interest, Increase from Business Combination	stgw_StockIssuedDuringPeriodValueNoncontrollingInterestIncreaseFromBusinessCombination	142,242,000
Net Income (Loss), Including Noncontrolling Interests, Equity Statement Impact	stgw_NetIncomeLossIncludingNoncontrollingInterestsEquityStatementImpact	24,742,000
Net Income (Loss), Including Noncontrolling Interests, Equity Statement Impact	stgw_NetIncomeLossIncludingNoncontrollingInterestsEquityStatementImpact	3,032,000
Net Income (Loss), Including Noncontrolling Interests, Equity Statement Impact	stgw_NetIncomeLossIncludingNoncontrollingInterestsEquityStatementImpact	(4,545,000)
Redeemable noncontrolling interest, changes in redemption value	stgw_Redeemablenoncontrollinginterestchangesinredemptionvalue	2,559,000
Redeemable noncontrolling interest, changes in redemption value	stgw_Redeemablenoncontrollinginterestchangesinredemptionvalue	(1,608,000)
Distribution Made to Limited Liability Company (LLC) Member, Cash Distributions Declared	us-gaap_DistributionMadeToLimitedLiabilityCompanyLLCMemberCashDistributionsDeclared	165,717,000
Contribution from Limited Liability Company (LLC)	stgw_ContributionFromLimitedLiabilityCompanyLLC	11,834,000
Stock Repurchased and Retired During Period, Value	us-gaap_StockRepurchasedAndRetiredDuringPeriodValue	820,000
Stockholders' Equity, Other	us-gaap_StockholdersEquityOther	228,000
Other Comprehensive Income (Loss), Net of Tax	us-gaap_OtherComprehensiveIncomeLossNetOfTax	12,537,000
Other Comprehensive Income (Loss), Net of Tax	us-gaap_OtherComprehensiveIncomeLossNetOfTax	(375,000)
Other Comprehensive Income (Loss), Net of Tax	us-gaap_OtherComprehensiveIncomeLossNetOfTax	(63,000)
Noncontrolling Interest [Member]
Stock Issued During Period, Value, Noncontrolling Interest, Increase from Business Combination	stgw_StockIssuedDuringPeriodValueNoncontrollingInterestIncreaseFromBusinessCombination	636,416,000
Net Income (Loss), Including Noncontrolling Interests, Equity Statement Impact	stgw_NetIncomeLossIncludingNoncontrollingInterestsEquityStatementImpact	2,693,000
Net Income (Loss), Including Noncontrolling Interests, Equity Statement Impact	stgw_NetIncomeLossIncludingNoncontrollingInterestsEquityStatementImpact	6,774,000
Net Income (Loss), Including Noncontrolling Interests, Equity Statement Impact	stgw_NetIncomeLossIncludingNoncontrollingInterestsEquityStatementImpact	70,000
Noncontrolling Interest, Decrease from Distributions to Noncontrolling Interest Holders	us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders	7,561,000
Noncontrolling Interest, Decrease from Distributions to Noncontrolling Interest Holders	us-gaap_MinorityInterestDecreaseFromDistributionsToNoncontrollingInterestHolders	934,000
Stockholders' Equity, Other	us-gaap_StockholdersEquityOther	173,000
Stockholders' Equity, Other	us-gaap_StockholdersEquityOther	(300,000)
Stockholders' Equity, Other	us-gaap_StockholdersEquityOther	161,000
Adjustments to Additional Paid in Capital, Changes due to Business Combinations	stgw_AdjustmentstoAdditionalPaidinCapitalChangesduetoBusinessCombinations	(10,450,000)
AOCI Attributable to Parent [Member]
Other Comprehensive Income (Loss), Net of Tax	us-gaap_OtherComprehensiveIncomeLossNetOfTax	$ 12,537,000
Preferred Stock [Member]
Stock Issued During Period, Noncontrolling Interest, Increase from Business Combination	stgw_StockIssuedDuringPeriodNoncontrollingInterestIncreaseFromBusinessCombination	123,849,000
Stock Issued During Period, Value, Noncontrolling Interest, Increase from Business Combination	stgw_StockIssuedDuringPeriodValueNoncontrollingInterestIncreaseFromBusinessCombination	$ 209,980,000
Additional Paid-in Capital [Member]
APIC, Share-Based Payment Arrangement, Increase for Cost Recognition	us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue	49,895,000
Stock Issued During Period, Value, Noncontrolling Interest, Increase from Business Combination	stgw_StockIssuedDuringPeriodValueNoncontrollingInterestIncreaseFromBusinessCombination	110,555,000
Stock Repurchased and Retired During Period, Value	us-gaap_StockRepurchasedAndRetiredDuringPeriodValue	820,000
Stockholders' Equity, Other	us-gaap_StockholdersEquityOther	(228,000)
Adjustments to Additional Paid in Capital, Changes due to Business Combinations	stgw_AdjustmentstoAdditionalPaidinCapitalChangesduetoBusinessCombinations	9,679,000
Member Units [Member]
Stock Issued During Period, Value, Noncontrolling Interest, Increase from Business Combination	stgw_StockIssuedDuringPeriodValueNoncontrollingInterestIncreaseFromBusinessCombination	(178,372,000)
Net Income (Loss), Including Noncontrolling Interests, Equity Statement Impact	stgw_NetIncomeLossIncludingNoncontrollingInterestsEquityStatementImpact	3,032,000
Net Income (Loss), Including Noncontrolling Interests, Equity Statement Impact	stgw_NetIncomeLossIncludingNoncontrollingInterestsEquityStatementImpact	24,742,000
Redeemable noncontrolling interest, changes in redemption value	stgw_Redeemablenoncontrollinginterestchangesinredemptionvalue	2,559,000
Distribution Made to Limited Liability Company (LLC) Member, Cash Distributions Declared	us-gaap_DistributionMadeToLimitedLiabilityCompanyLLCMemberCashDistributionsDeclared	165,717,000
Contribution from Limited Liability Company (LLC)	stgw_ContributionFromLimitedLiabilityCompanyLLC	11,834,000
Other Comprehensive Income (Loss), Net of Tax	us-gaap_OtherComprehensiveIncomeLossNetOfTax	(375,000)
Other Comprehensive Income (Loss), Net of Tax	us-gaap_OtherComprehensiveIncomeLossNetOfTax	$ (63,000)
Common Class A and B [Member]
Stock Repurchased and Retired During Period, Shares	us-gaap_StockRepurchasedAndRetiredDuringPeriodShares	12,000
Common Class A and B [Member] | Common Stock [Member]
Stock Issued During Period, Noncontrolling Interest, Increase from Business Combination	stgw_StockIssuedDuringPeriodNoncontrollingInterestIncreaseFromBusinessCombination	78,794,000
Stock Issued During Period, Value, Noncontrolling Interest, Increase from Business Combination	stgw_StockIssuedDuringPeriodValueNoncontrollingInterestIncreaseFromBusinessCombination	$ 77,000
Stock Issued During Period, Shares, Restricted Stock Award, Gross	us-gaap_StockIssuedDuringPeriodSharesRestrictedStockAwardGross	202,000
Common Class C [Member] | Common Stock [Member]
Stock Issued During Period, Noncontrolling Interest, Increase from Business Combination	stgw_StockIssuedDuringPeriodNoncontrollingInterestIncreaseFromBusinessCombination	179,970,000
Stock Issued During Period, Value, Noncontrolling Interest, Increase from Business Combination	stgw_StockIssuedDuringPeriodValueNoncontrollingInterestIncreaseFromBusinessCombination	$ 2,000