Subgroups — #3744

Order 144.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic
2	#634	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#204	—	3	4	no	maximal
5	C₂×C₃⋊D₃	—	2	1	no	—
6	C₃²×C₄	C₂²	1	1	yes	characteristic
7	C₃⋊Dic₃	—	2	1	no	—
8	D₁₂	—	3	4	no	—
9	Dic₆	—	3	4	no	—
10	C₃×C₈	D₃	1	4	yes	complemented
11	C₂×C₃²	D₄	1	1	yes	characteristic
12	C₃⋊D₃	—	4	1	no	—
13	SD₁₆	—	9	1	no	Sylow
14	C₂×D₃	—	6	4	no	—
15	C₃×C₄	C₂×D₃	1	4	yes	—
16	Dic₃	—	6	4	no	—
17	C₃²	SD₁₆	1	1	yes	characteristic, complemented, Sylow
18	Q₈	—	9	1	no	—
19	D₄	—	9	1	no	—
20	C₈	C₃⋊D₃	1	1	yes	characteristic, complemented
21	C₂×C₃	D₁₂	1	4	yes	—
22	D₃	—	12	4	no	—
23	C₂²	—	18	1	no	—
24	C₄	—	18	1	no	—
25	C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
26	C₃	#204	1	4	yes	complemented
27	C₂	—	36	1	no	—
28	C₂	C₄⋊(C₃⋊D₃)	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.