Subgroups — C₃³×D₄ #6314

Order 216.

224 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center, socle	C₂×C₃³	C₂²
commutator, Frattini, cosocle	C₂	C₂²×C₃³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃³ ◁ G

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.