Subgroups — C₄⋊(C₃⋊(C₃⋊D₃)) #6310

Order 216.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊(C₃⋊D₃)	C₂	1	2	yes	maximal, complemented
2	C₃³×C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊(C₃⋊D₃)	—	3	13	no	maximal
4	C₂×C₃³	C₂²	1	1	yes	characteristic
5	C₃⋊(C₃⋊D₃)	—	2	2	no	—
6	C₂×C₃⋊D₃	—	3	26	no	—
7	C₃²×C₄	D₃	1	13	yes	complemented
8	C₃³	D₄	1	1	yes	characteristic, complemented, Sylow
9	D₁₂	—	9	13	no	—
10	C₂×C₃²	C₂×D₃	1	13	yes	—
11	C₃⋊D₃	—	6	26	no	—
12	C₂×D₃	—	9	26	no	—
13	C₃×C₄	C₃⋊D₃	1	13	yes	complemented
14	C₃²	D₁₂	1	13	yes	complemented
15	D₄	—	27	1	no	Sylow
16	C₂×C₃	C₂×C₃⋊D₃	1	13	yes	—
17	D₃	—	18	26	no	—
18	C₂²	—	27	2	no	—
19	C₄	C₃⋊(C₃⋊D₃)	1	1	yes	characteristic, complemented
20	C₃	C₄⋊(C₃⋊D₃)	1	13	yes	complemented
21	C₂	—	54	2	no	—
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.