Subgroups — C₃²×#1094 #11758108

Order 972.

788 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃⁴	C₃	1	1	yes	maximal, characteristic
2	C₃×#1094	C₃	1	36	yes	maximal, direct product factor
3	C₃²×C₂²⋊C₉	C₃	1	3	yes	maximal, complemented
4	C₃²×3₋¹⁺²	—	4	1	no	maximal, Sylow
5	C₂×C₃⁴	—	3	1	no	—
6	C₂²×C₃³	—	3	9	no	—
7	C₂²×C₃³	C₃²	1	12	yes	—
8	C₂²×C₃³	C₃²	1	1	yes	characteristic
9	#1094	C₃²	1	81	yes	direct product factor
10	C₃×C₂²⋊C₉	C₃²	1	36	yes	complemented
11	C₃⁴	A₄	1	1	yes	characteristic
12	C₃×3₋¹⁺²	—	4	36	no	—
13	C₃²×C₉	—	4	3	no	—
14	C₂×C₃³	—	3	27	no	—
15	C₂×C₃³	—	3	12	no	—
16	C₂×C₃³	—	3	1	no	—
17	C₂²×C₃²	—	3	36	no	—
18	C₂²×C₃²	3₋¹⁺²	1	9	yes	complemented
19	C₂²×C₃²	C₃³	1	9	yes	—
20	C₂²×C₃²	C₃³	1	4	yes	—
21	C₂²⋊C₉	C₃³	1	27	yes	complemented
22	C₃³	—	3	9	no	—
23	C₃³	C₃×A₄	1	12	yes	—
24	C₃³	C₃×A₄	1	1	yes	characteristic
25	3₋¹⁺²	—	4	81	no	—
26	C₃×C₉	—	4	36	no	—
27	C₂×C₃²	—	3	108	no	—
28	C₂×C₃²	—	3	9	no	—
29	C₂×C₃²	—	3	9	no	—
30	C₂×C₃²	—	3	4	no	—
31	C₂²×C₃	—	3	9	no	—
32	C₂²×C₃	C₃×3₋¹⁺²	1	12	yes	complemented
33	C₂²×C₃	C₃⁴	1	1	yes	characteristic
34	C₃²	—	3	36	no	—
35	C₃²	#1094	1	9	yes	direct product factor
36	C₃²	C₃²×A₄	1	9	yes	—
37	C₃²	C₃²×A₄	1	4	yes	—
38	C₉	—	4	27	no	—
39	C₂×C₃	—	3	27	no	—
40	C₂×C₃	—	3	12	no	—
41	C₂×C₃	—	3	1	no	—
42	C₂²	C₃²×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
43	C₃	—	3	9	no	—
44	C₃	C₃×#1094	1	12	yes	direct product factor
45	C₃	C₃³×A₄	1	1	yes	characteristic
46	C₂	—	3	1	no	—

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.