Subgroups — C₂×#1094 #6269

Order 216.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#1094	C₂	1	1	yes	maximal, characteristic, direct product factor
2	C₂³×C₃²	C₃	1	1	yes	maximal, characteristic
3	C₂×C₂²⋊C₉	C₃	1	3	yes	maximal, complemented
4	C₂×3₋¹⁺²	—	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
8	C₂²⋊C₉	C₂×C₃	1	3	yes	complemented
9	3₋¹⁺²	—	4	1	no	Sylow
10	C₂³×C₃	—	3	1	no	—
11	C₂³×C₃	C₃²	1	1	yes	characteristic
12	C₂×C₃²	—	3	1	no	—
13	C₂×C₃²	—	3	1	no	—
14	C₂×C₃²	A₄	1	1	yes	characteristic
15	C₂×C₉	—	4	3	no	—
16	C₂²×C₃	—	3	1	no	—
17	C₂²×C₃	—	3	3	no	—
18	C₂²×C₃	—	3	3	no	—
19	C₂²×C₃	—	3	1	no	—
20	C₂²×C₃	—	3	1	no	—
21	C₂²×C₃	C₂×C₃²	1	1	yes	characteristic
22	C₃²	C₂×A₄	1	1	yes	characteristic
23	C₉	—	4	3	no	—
24	C₂³	3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃	—	3	3	no	—
26	C₂×C₃	—	3	3	no	—
27	C₂×C₃	—	3	1	no	—
28	C₂×C₃	—	3	1	no	—
29	C₂×C₃	—	3	1	no	—
30	C₂×C₃	C₃×A₄	1	1	yes	characteristic
31	C₂²	—	3	1	no	—
32	C₂²	—	3	1	no	—
33	C₂²	C₂×3₋¹⁺²	1	1	yes	characteristic, complemented
34	C₃	—	3	1	no	—
35	C₃	C₂×C₃×A₄	1	1	yes	characteristic
36	C₂	—	3	1	no	—
37	C₂	—	3	1	no	—
38	C₂	#1094	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.