Subgroups — C₄⋊#272 #6231

Order 216.

88 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#272	C₂	1	2	yes	maximal, complemented
2	C₄×H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₁₂	—	3	4	no	maximal
4	C₂×H(3,𝔽₃)	C₂²	1	1	yes	characteristic
5	#272	—	2	2	no	—
6	C₂×C₃×D₃	—	3	8	no	—
7	C₃²×C₄	D₃	1	4	yes	complemented
8	H(3,𝔽₃)	D₄	1	1	yes	characteristic, complemented, Sylow
9	C₃×D₄	—	9	1	no	—
10	D₁₂	—	3	4	no	—
11	C₂×C₃²	C₂×D₃	1	4	yes	—
12	C₃×D₃	—	6	8	no	—
13	C₂²×C₃	—	9	2	no	—
14	C₂×D₃	—	3	8	no	—
15	C₃×C₄	—	3	4	no	—
16	C₃×C₄	C₃⋊D₃	1	1	yes	characteristic
17	C₃²	D₁₂	1	4	yes	complemented
18	D₄	—	9	1	no	Sylow
19	C₂×C₃	—	3	4	no	—
20	C₂×C₃	—	18	2	no	—
21	C₂×C₃	C₂×C₃⋊D₃	1	1	yes	characteristic
22	D₃	—	6	8	no	—
23	C₂²	—	9	2	no	—
24	C₄	#272	1	1	yes	characteristic, complemented
25	C₃	—	3	4	no	—
26	C₃	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
27	C₂	—	18	2	no	—
28	C₂	C₂×#272	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.