Subgroups — #6226

Order 216.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊Dic₉	C₂	1	2	yes	maximal
3	#634	—	3	1	no	maximal
4	Dic₁₈	—	3	3	no	maximal
5	C₂×C₃×C₉	C₂²	1	1	yes	characteristic
6	C₃²×C₄	D₃	1	1	yes	characteristic
7	C₃⋊Dic₃	—	3	2	no	—
8	C₄×C₉	D₃	1	3	yes	—
9	Dic₉	—	3	6	no	—
10	C₃×C₉	Q₈	1	1	yes	characteristic, complemented, Sylow
11	Dic₆	—	9	3	no	—
12	Dic₆	—	9	1	no	—
13	C₂×C₃²	C₂×D₃	1	1	yes	characteristic
14	C₂×C₉	C₂×D₃	1	3	yes	—
15	C₃×C₄	D₉	1	3	yes	—
16	C₃×C₄	C₃⋊D₃	1	1	yes	characteristic
17	Dic₃	—	9	6	no	—
18	Dic₃	—	9	2	no	—
19	C₃²	Dic₆	1	1	yes	characteristic
20	C₉	Dic₆	1	3	yes	complemented
21	Q₈	—	27	1	no	Sylow
22	C₂×C₃	C₂×D₉	1	3	yes	—
23	C₂×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
24	C₄	—	27	2	no	—
25	C₄	C₃⋊D₉	1	1	yes	characteristic
26	C₃	Dic₁₈	1	3	yes	complemented
27	C₃	#634	1	1	yes	characteristic
28	C₂	C₂×C₃⋊D₉	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.