Subgroups — C₃×#634 #6303

Order 216.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃³×C₄	C₂	1	1	yes	maximal, characteristic
2	C₃×C₃⋊Dic₃	C₂	1	2	yes	maximal
3	#634	C₃	1	1	yes	maximal, characteristic, direct product factor
4	C₃×Dic₆	—	3	4	no	maximal
5	C₂×C₃³	C₂²	1	1	yes	characteristic
6	C₃²×C₄	—	2	4	no	—
7	C₃²×C₄	D₃	1	4	yes	—
8	C₃²×C₄	C₂×C₃	1	1	yes	characteristic
9	C₃⋊Dic₃	C₂×C₃	1	2	yes	—
10	C₃×Dic₃	—	3	8	no	—
11	C₃³	Q₈	1	1	yes	characteristic, complemented, Sylow
12	C₃×Q₈	—	9	1	no	—
13	Dic₆	—	3	4	no	—
14	C₂×C₃²	—	2	4	no	—
15	C₂×C₃²	C₂×D₃	1	4	yes	—
16	C₂×C₃²	C₂²×C₃	1	1	yes	characteristic
17	C₃×C₄	—	2	4	no	—
18	C₃×C₄	—	9	2	no	—
19	C₃×C₄	C₃×D₃	1	4	yes	—
20	C₃×C₄	C₃⋊D₃	1	1	yes	characteristic
21	Dic₃	—	3	8	no	—
22	C₃²	—	2	4	no	—
23	C₃²	Dic₆	1	4	yes	complemented
24	C₃²	C₃×Q₈	1	1	yes	characteristic, complemented
25	Q₈	—	9	1	no	Sylow
26	C₂×C₃	—	2	4	no	—
27	C₂×C₃	C₂×C₃×D₃	1	4	yes	—
28	C₂×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
29	C₄	—	9	2	no	—
30	C₄	C₃×C₃⋊D₃	1	1	yes	characteristic
31	C₃	—	2	4	no	—
32	C₃	C₃×Dic₆	1	4	yes	complemented
33	C₃	#634	1	1	yes	characteristic, direct product factor
34	C₂	C₂×C₃×C₃⋊D₃	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.