Subgroups — C₉×SL(2,𝔽₃) #6201

Order 216.

33 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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