Subgroups — #6204

Order 216.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×Q₈	C₃	1	1	yes	maximal, characteristic
2	Q₈⋊C₉	C₃	1	3	yes	maximal, complemented
3	C₂×3₋¹⁺²	—	4	1	no	maximal
4	C₃²×C₄	—	3	1	no	—
5	3₋¹⁺²	—	4	1	no	Sylow
6	C₃×Q₈	—	3	1	no	—
7	C₃×Q₈	C₃²	1	1	yes	characteristic
8	C₂×C₃²	A₄	1	1	yes	characteristic
9	C₂×C₉	—	4	3	no	—
10	C₃×C₄	—	3	3	no	—
11	C₃×C₄	—	3	1	no	—
12	C₃²	SL(2,𝔽₃)	1	1	yes	characteristic
13	C₉	—	4	3	no	—
14	Q₈	3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₃	—	3	1	no	—
16	C₂×C₃	C₃×A₄	1	1	yes	characteristic
17	C₄	—	3	1	no	—
18	C₃	—	3	1	no	—
19	C₃	C₃×SL(2,𝔽₃)	1	1	yes	characteristic
20	C₂	#1094	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. Q₈⋊C₉	C₃	semidirect
14. Q₈	3₋¹⁺²	semidirect

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