Subgroups — C₃²×#168 #67103

Order 360.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₄×C₅	C₂	1	1	yes	maximal, characteristic
2	C₃×#168	C₃	1	4	yes	maximal, direct product factor
3	C₂×C₃²×C₅	C₄	1	1	yes	characteristic
4	C₃²×C₈	—	5	1	no	maximal, Hall
5	C₃×C₄×C₅	C₂×C₃	1	4	yes	—
6	C₃²×C₅	C₈	1	1	yes	characteristic, complemented, Hall
7	#168	C₃²	1	1	yes	characteristic, direct product factor, Hall
8	C₃²×C₄	D₅	1	1	yes	characteristic
9	C₂×C₃×C₅	C₃×C₄	1	4	yes	—
10	C₃×C₈	—	5	4	no	—
11	C₄×C₅	C₂×C₃²	1	1	yes	characteristic
12	C₂×C₃²	Dic₅	1	1	yes	characteristic
13	C₃×C₅	C₃×C₈	1	4	yes	complemented
14	C₃×C₄	C₃×D₅	1	4	yes	—
15	C₂×C₅	C₃²×C₄	1	1	yes	characteristic
16	C₃²	#168	1	1	yes	characteristic, direct product factor, Sylow
17	C₈	—	5	1	no	Sylow
18	C₂×C₃	C₃×Dic₅	1	4	yes	—
19	C₅	C₃²×C₈	1	1	yes	characteristic, complemented, Sylow
20	C₄	C₃²×D₅	1	1	yes	characteristic
21	C₃	C₃×#168	1	4	yes	direct product factor
22	C₂	C₃²×Dic₅	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.