Subgroups — C₂×3₋¹⁺²⋊C₄ #6224

Order 216.

53 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×3₋¹⁺²	C₂	1	1	yes	maximal, characteristic
2	3₋¹⁺²⋊C₄	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃×Dic₃	—	3	1	no	maximal
4	C₂×Dic₉	C₃	1	1	yes	maximal, characteristic, complemented
5	C₂×3₋¹⁺²	C₄	1	2	yes	complemented
6	C₂×3₋¹⁺²	C₂²	1	1	yes	characteristic
7	C₂²×C₃²	D₃	1	1	yes	characteristic
8	C₃×Dic₃	—	3	2	no	—
9	C₂²×C₉	—	2	1	no	—
10	C₂²×C₉	C₂×C₃	1	1	yes	characteristic
11	Dic₉	C₂×C₃	1	2	yes	complemented
12	3₋¹⁺²	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₃×C₄	—	9	1	no	—
14	C₂×Dic₃	—	3	1	no	—
15	C₂×C₃²	Dic₃	1	2	yes	—
16	C₂×C₃²	C₂×D₃	1	1	yes	characteristic
17	C₂×C₉	—	2	2	no	—
18	C₂×C₉	—	2	1	no	—
19	C₂×C₉	C₃×C₄	1	2	yes	complemented
20	C₂×C₉	C₂²×C₃	1	1	yes	characteristic
21	C₂²×C₃	—	3	1	no	—
22	C₂²×C₃	C₃×D₃	1	1	yes	characteristic
23	C₃×C₄	—	9	2	no	—
24	Dic₃	—	3	2	no	—
25	C₃²	C₂×Dic₃	1	1	yes	characteristic
26	C₉	—	2	1	no	—
27	C₉	C₂×C₃×C₄	1	1	yes	characteristic, complemented
28	C₂×C₄	—	9	1	no	Sylow
29	C₂×C₃	—	3	2	no	—
30	C₂×C₃	—	3	1	no	—
31	C₂×C₃	C₃×Dic₃	1	2	yes	—
32	C₂×C₃	C₂×C₃×D₃	1	1	yes	characteristic
33	C₂²	AGL(1,ℤ/9)	1	1	yes	characteristic
34	C₄	—	9	2	no	—
35	C₃	—	3	1	no	—
36	C₃	C₂×C₃×Dic₃	1	1	yes	characteristic
37	C₂	3₋¹⁺²⋊C₄	1	2	yes	direct product factor
38	C₂	C₂×AGL(1,ℤ/9)	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.