Subgroups — C₂×C₂²⋊H(3,𝔽₃) #6270

Order 216.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊H(3,𝔽₃)	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂³×C₃²	C₃	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×A₄	C₃	1	3	yes	maximal, complemented
4	C₂×H(3,𝔽₃)	—	4	1	no	maximal
5	C₂²×C₃²	—	3	1	no	—
6	C₂²×C₃²	—	3	1	no	—
7	C₂²×C₃²	C₂×C₃	1	1	yes	characteristic, complemented
8	C₃×A₄	C₂×C₃	1	3	yes	complemented
9	H(3,𝔽₃)	—	4	1	no	Sylow
10	C₂³×C₃	—	3	1	no	—
11	C₂³×C₃	C₃²	1	1	yes	characteristic
12	C₂×A₄	—	3	3	no	—
13	C₂×C₃²	—	3	1	no	—
14	C₂×C₃²	—	3	1	no	—
15	C₂×C₃²	—	4	3	no	—
16	C₂×C₃²	A₄	1	1	yes	characteristic, complemented
17	C₂²×C₃	—	3	1	no	—
18	C₂²×C₃	—	3	3	no	—
19	C₂²×C₃	—	3	3	no	—
20	C₂²×C₃	—	3	1	no	—
21	C₂²×C₃	—	3	1	no	—
22	C₂²×C₃	C₂×C₃²	1	1	yes	characteristic
23	A₄	—	3	3	no	—
24	C₃²	—	4	3	no	—
25	C₃²	C₂×A₄	1	1	yes	characteristic, complemented
26	C₂³	H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
27	C₂×C₃	—	3	3	no	—
28	C₂×C₃	—	3	3	no	—
29	C₂×C₃	—	3	1	no	—
30	C₂×C₃	—	3	1	no	—
31	C₂×C₃	—	3	1	no	—
32	C₂×C₃	—	12	3	no	—
33	C₂×C₃	C₃×A₄	1	1	yes	characteristic
34	C₂²	—	3	1	no	—
35	C₂²	—	3	1	no	—
36	C₂²	C₂×H(3,𝔽₃)	1	1	yes	characteristic, complemented
37	C₃	—	3	1	no	—
38	C₃	—	12	3	no	—
39	C₃	C₂×C₃×A₄	1	1	yes	characteristic
40	C₂	—	3	1	no	—
41	C₂	—	3	1	no	—
42	C₂	C₂²⋊H(3,𝔽₃)	1	1	yes	characteristic, direct product factor

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.