Share-Based Compensation - Schedule of Stock Units Activity (Detail) $ in Millions	9 Months Ended
Mar. 26, 2022 USD ($) shares
Restricted stock units outstanding [Member]
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Stock Unit Awards Outstanding, Balance as of June 2021	1,323,286
Stock Unit Awards, Granted	602,320
Stock Unit Awards, Delivered/Released	(549,596)
Stock Unit Awards, Forfeited	(147,461)
Stock Unit Awards Outstanding, Balance as of March 2022	1,228,549
Aggregate Intrinsic Value, Balance as of March 2022 \| $	$ 267.2
Market stock units outstanding [Member]
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Stock Unit Awards Outstanding, Balance as of June 2021	347,027
Stock Unit Awards, Granted	134,728
Stock Unit Awards, Delivered/Released	(203,883)
Stock Unit Awards, Forfeited	(25,898)
Stock Unit Awards Outstanding, Balance as of March 2022	251,974
Aggregate Intrinsic Value, Balance as of March 2022 \| $	$ 54.8
Performance stock units outstanding [Member]
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Stock Unit Awards Outstanding, Balance as of June 2021	317,392
Stock Unit Awards, Granted	185,676
Stock Unit Awards, Delivered/Released	(208,023)
Stock Unit Awards, Forfeited	(37,142)
Stock Unit Awards Outstanding, Balance as of March 2022	257,903
Aggregate Intrinsic Value, Balance as of March 2022 \| $	$ 56.1
Phantom Stock Unit [Member]
Share Based Compensation Arrangement By Share Based Payment Award [Line Items]
Stock Unit Awards Outstanding, Balance as of June 2021	402,458
Stock Unit Awards, Delivered/Released	(196,420)
Stock Unit Awards, Forfeited	(25,845)
Stock Unit Awards Outstanding, Balance as of March 2022	180,193

The number of equity-based payment instruments, excluding stock (or unit) options, that were forfeited during the reporting period.

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(1)(iv)(3)
-URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsForfeitedInPeriod
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

The number of grants made during the period on other than stock (or unit) option plans (for example, phantom stock or unit plan, stock or unit appreciation rights plan, performance target plan).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(iii)(1)
-URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsGrantsInPeriod
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

The number of non-vested equity-based payment instruments, excluding stock (or unit) options, that validly exist and are outstanding as of the balance sheet date.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(i)-(ii)
-URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsNonvestedNumber
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant

- Definition

The number of equity-based payment instruments, excluding stock (or unit) options, that vested during the reporting period.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 718
-SubTopic 10
-Section 50
-Paragraph 2
-Subparagraph (c)(2)(iii)(2)
-URI http://asc.fasb.org/extlink&oid=120381028&loc=d3e5070-113901

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardEquityInstrumentsOtherThanOptionsVestedInPeriod
Namespace Prefix:	us-gaap_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	duration

- Definition

Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

+ References

No definition available.

+ Details

Name:	us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardLineItems
Namespace Prefix:	us-gaap_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

- Definition

Intrinsic value of outstanding award under share-based payment arrangement. Excludes share and unit options.

+ References

No definition available.

+ Details

Name:	us-gaap_SharebasedCompensationArrangementBySharebasedPaymentAwardEquityInstrumentsOtherThanOptionsAggregateIntrinsicValueOutstanding
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

- Details

Name:	us-gaap_AwardTypeAxis=us-gaap_RestrictedStockUnitsRSUMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AwardTypeAxis=syna_MarketStockUnitsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AwardTypeAxis=syna_PerformanceStockUnitsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type:

- Details

Name:	us-gaap_AwardTypeAxis=us-gaap_PhantomShareUnitsPSUsMember
Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: