Subgroups — C₃×#627 #6286

Order 216.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃⋊Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×Dic₃	C₂	1	2	yes	maximal
3	C₃×Dic₆	—	3	2	no	maximal
4	#627	C₃	1	1	yes	maximal, characteristic, direct product factor
5	C₂×C₃³	C₂²	1	1	yes	characteristic
6	C₃²×C₄	—	3	2	no	—
7	C₃⋊Dic₃	C₂×C₃	1	1	yes	characteristic
8	C₃×Dic₃	—	2	2	no	—
9	C₃×Dic₃	—	3	2	no	—
10	C₃×Dic₃	—	6	1	no	—
11	C₃×Dic₃	D₃	1	2	yes	—
12	C₃×Dic₃	C₂×C₃	1	2	yes	—
13	C₃³	Q₈	1	1	yes	characteristic, complemented, Sylow
14	C₃×Q₈	—	9	1	no	—
15	Dic₆	—	3	2	no	—
16	C₂×C₃²	—	2	1	no	—
17	C₂×C₃²	—	2	2	no	—
18	C₂×C₃²	—	4	1	no	—
19	C₂×C₃²	C₂×D₃	1	2	yes	—
20	C₂×C₃²	C₂²×C₃	1	1	yes	characteristic
21	C₃×C₄	—	3	2	no	—
22	C₃×C₄	—	3	2	no	—
23	C₃×C₄	—	6	2	no	—
24	C₃×C₄	—	9	1	no	—
25	Dic₃	—	3	2	no	—
26	Dic₃	—	6	1	no	—
27	Dic₃	C₃×D₃	1	2	yes	—
28	C₃²	—	2	1	no	—
29	C₃²	—	2	2	no	—
30	C₃²	—	4	1	no	—
31	C₃²	Dic₆	1	2	yes	complemented
32	C₃²	C₃×Q₈	1	1	yes	characteristic, complemented
33	Q₈	—	9	1	no	Sylow
34	C₂×C₃	—	2	1	no	—
35	C₂×C₃	—	2	2	no	—
36	C₂×C₃	—	4	1	no	—
37	C₂×C₃	D₃²	1	1	yes	characteristic
38	C₂×C₃	C₂×C₃×D₃	1	2	yes	—
39	C₄	—	3	2	no	—
40	C₄	—	9	1	no	—
41	C₃	—	2	2	no	—
42	C₃	—	2	1	no	—
43	C₃	—	4	1	no	—
44	C₃	#627	1	1	yes	characteristic, direct product factor
45	C₃	C₃×Dic₆	1	2	yes	complemented
46	C₂	C₃×D₃²	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.