Subgroups — C₂×C₃×#157 #6331

Order 216.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	C₃×#157	C₂	1	2	yes	maximal, direct product factor
3	C₂×#157	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₂×C₃³	C₄	1	1	yes	characteristic, complemented
5	C₃×C₃⋊D₃	C₄	1	1	yes	characteristic, complemented
6	C₃×C₃⋊D₃	C₂²	1	1	yes	characteristic
7	C₂×C₃⋊D₃	C₂×C₃	1	1	yes	characteristic
8	C₂×C₃×D₃	—	6	2	no	—
9	#157	C₂×C₃	1	2	yes	direct product factor
10	C₃³	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
11	C₂×C₃×C₄	—	9	1	no	maximal
12	C₂×C₃²	—	2	2	no	—
13	C₂×C₃²	—	4	2	no	—
14	C₂×C₃²	C₃×C₄	1	1	yes	characteristic, complemented
15	C₃⋊D₃	C₃×C₄	1	1	yes	characteristic, complemented
16	C₃⋊D₃	C₂²×C₃	1	1	yes	characteristic
17	C₃×D₃	—	6	2	no	—
18	C₃×D₃	—	6	2	no	—
19	C₂²×C₃	—	9	1	no	—
20	C₂×D₃	—	6	2	no	—
21	C₃×C₄	—	9	2	no	—
22	C₃²	—	2	2	no	—
23	C₃²	—	4	2	no	—
24	C₃²	C₂×C₃×C₄	1	1	yes	characteristic, complemented
25	C₂×C₄	—	9	1	no	Sylow
26	C₂×C₃	—	2	2	no	—
27	C₂×C₃	—	4	2	no	—
28	C₂×C₃	—	9	1	no	—
29	C₂×C₃	—	9	1	no	—
30	C₂×C₃	#157	1	1	yes	characteristic, direct product factor
31	D₃	—	6	2	no	—
32	D₃	—	6	2	no	—
33	C₂²	—	9	1	no	—
34	C₄	—	9	2	no	—
35	C₃	—	2	2	no	—
36	C₃	—	4	2	no	—
37	C₃	C₂×#157	1	1	yes	characteristic, direct product factor
38	C₂	—	9	1	no	—
39	C₂	—	9	1	no	—
40	C₂	C₃×#157	1	1	yes	characteristic, direct product factor

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.