Subgroups — #6312

Order 216.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃⋊(C₃⋊D₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃⋊(C₃⋊Dic₃)	C₂	1	1	yes	maximal, characteristic, complemented
4	#638	—	3	13	no	maximal
5	C₂×C₃³	—	2	1	no	—
6	C₂×C₃³	C₂²	1	1	yes	characteristic
7	C₃⋊(C₃⋊D₃)	—	2	1	no	—
8	C₂²×C₃²	D₃	1	13	yes	complemented
9	C₂×C₃⋊D₃	—	3	13	no	—
10	C₃⋊Dic₃	—	3	13	no	—
11	C₃³	D₄	1	1	yes	characteristic, complemented, Sylow
12	#67	—	9	13	no	—
13	C₂×C₃²	—	2	13	no	—
14	C₂×C₃²	C₂×D₃	1	13	yes	—
15	C₃⋊D₃	—	6	13	no	—
16	C₂²×C₃	C₃⋊D₃	1	13	yes	complemented
17	C₂×D₃	—	9	13	no	—
18	Dic₃	—	9	13	no	—
19	C₃²	#67	1	13	yes	complemented
20	D₄	—	27	1	no	Sylow
21	C₂×C₃	—	2	13	no	—
22	C₂×C₃	C₂×C₃⋊D₃	1	13	yes	—
23	D₃	—	18	13	no	—
24	C₂²	—	27	1	no	—
25	C₂²	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
26	C₄	—	27	1	no	—
27	C₃	#638	1	13	yes	complemented
28	C₂	—	2	1	no	—
29	C₂	—	54	1	no	—
30	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.