Subgroups — C₄×C₃⋊(C₃⋊D₃) #6309

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