Subgroups — C₂×C₃⋊(C₃⋊Dic₃) #6311

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
2	C₃⋊(C₃⋊Dic₃)	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃⋊Dic₃	—	3	13	no	maximal
4	C₂×C₃³	C₄	1	2	yes	complemented
5	C₂×C₃³	C₂²	1	1	yes	characteristic
6	C₂²×C₃²	D₃	1	13	yes	—
7	C₃⋊Dic₃	—	3	26	no	—
8	C₃³	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
9	C₂×Dic₃	—	9	13	no	—
10	C₂×C₃²	Dic₃	1	26	yes	complemented
11	C₂×C₃²	C₂×D₃	1	13	yes	—
12	C₂²×C₃	C₃⋊D₃	1	13	yes	—
13	Dic₃	—	9	26	no	—
14	C₃²	C₂×Dic₃	1	13	yes	complemented
15	C₂×C₄	—	27	1	no	Sylow
16	C₂×C₃	C₃⋊Dic₃	1	26	yes	complemented
17	C₂×C₃	C₂×C₃⋊D₃	1	13	yes	—
18	C₂²	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic
19	C₄	—	27	2	no	—
20	C₃	C₂×C₃⋊Dic₃	1	13	yes	complemented
21	C₂	C₃⋊(C₃⋊Dic₃)	1	2	yes	direct product factor
22	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.