Subgroups — #3746

Order 144.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#634	C₂	1	2	yes	maximal
2	C₃²×C₈	C₂	1	1	yes	maximal, characteristic
3	Dic₁₂	—	3	4	no	maximal
4	C₃²×C₄	C₂²	1	1	yes	characteristic
5	C₃⋊Dic₃	—	2	2	no	—
6	Dic₆	—	3	8	no	—
7	C₃×C₈	D₃	1	4	yes	—
8	C₂×C₃²	D₄	1	1	yes	characteristic
9	Q₁₆	—	9	1	no	Sylow
10	C₃×C₄	C₂×D₃	1	4	yes	—
11	Dic₃	—	6	8	no	—
12	C₃²	Q₁₆	1	1	yes	characteristic, complemented, Sylow
13	Q₈	—	9	2	no	—
14	C₈	C₃⋊D₃	1	1	yes	characteristic
15	C₂×C₃	D₁₂	1	4	yes	—
16	C₄	—	18	2	no	—
17	C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
18	C₃	Dic₁₂	1	4	yes	complemented
19	C₂	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. C₃²	Q₁₆	semidirect
18. C₃	Dic₁₂	semidirect

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