Subgroups — #634⋊C₃ #6212

Order 216.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic
2	(C₃⋊Dic₃)⋊C₃	C₂	1	2	yes	maximal
3	#634	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃×Dic₆	—	3	1	no	maximal
5	C₂×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
6	C₃²×C₄	—	2	1	no	—
7	C₃²×C₄	D₃	1	1	yes	characteristic
8	C₃²×C₄	C₂×C₃	1	1	yes	characteristic
9	C₃⋊Dic₃	C₂×C₃	1	2	yes	—
10	C₃×Dic₃	—	3	2	no	—
11	H(3,𝔽₃)	Q₈	1	1	yes	characteristic, complemented, Sylow
12	C₃×Q₈	—	9	1	no	—
13	Dic₆	—	3	1	no	—
14	Dic₆	—	9	1	no	—
15	C₂×C₃²	—	2	1	no	—
16	C₂×C₃²	C₂×D₃	1	1	yes	characteristic
17	C₂×C₃²	C₂²×C₃	1	1	yes	characteristic
18	C₃×C₄	—	3	1	no	—
19	C₃×C₄	—	3	1	no	—
20	C₃×C₄	—	6	1	no	—
21	C₃×C₄	—	9	2	no	—
22	C₃×C₄	C₃×D₃	1	1	yes	characteristic
23	Dic₃	—	3	2	no	—
24	Dic₃	—	9	2	no	—
25	C₃²	—	2	1	no	—
26	C₃²	Dic₆	1	1	yes	characteristic, complemented
27	C₃²	C₃×Q₈	1	1	yes	characteristic, complemented
28	Q₈	—	9	1	no	Sylow
29	C₂×C₃	—	3	1	no	—
30	C₂×C₃	—	3	1	no	—
31	C₂×C₃	—	6	1	no	—
32	C₂×C₃	C₂×C₃×D₃	1	1	yes	characteristic
33	C₄	—	9	2	no	—
34	C₄	(C₃⋊D₃)⋊C₃	1	1	yes	characteristic
35	C₃	—	3	1	no	—
36	C₃	—	3	1	no	—
37	C₃	—	6	1	no	—
38	C₃	C₃×Dic₆	1	1	yes	characteristic
39	C₂	C₂×(C₃⋊D₃)⋊C₃	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.