Subgroups — C₃³×C₂²⋊C₉ #11758107

Order 972.

1004 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	C₃²×C₂²⋊C₉	C₃	1	39	yes	maximal, direct product factor
3	C₃³×C₉	—	4	1	no	maximal, Sylow
4	C₂×C₃⁴	—	3	1	no	—
5	C₂²×C₃³	C₉	1	27	yes	complemented
6	C₂²×C₃³	C₃²	1	13	yes	—
7	C₃×C₂²⋊C₉	C₃²	1	117	yes	direct product factor
8	C₃⁴	A₄	1	1	yes	characteristic
9	C₃²×C₉	—	4	39	no	—
10	C₂×C₃³	—	3	27	no	—
11	C₂×C₃³	—	3	13	no	—
12	C₂²×C₃²	C₃×C₉	1	117	yes	complemented
13	C₂²×C₃²	C₃³	1	13	yes	—
14	C₂²⋊C₉	C₃³	1	27	yes	direct product factor
15	C₃³	C₂²⋊C₉	1	27	yes	direct product factor
16	C₃³	C₃×A₄	1	13	yes	—
17	C₃×C₉	—	4	117	no	—
18	C₂×C₃²	—	3	117	no	—
19	C₂×C₃²	—	3	13	no	—
20	C₂²×C₃	C₃²×C₉	1	39	yes	complemented
21	C₂²×C₃	C₃⁴	1	1	yes	characteristic
22	C₃²	C₃×C₂²⋊C₉	1	117	yes	direct product factor
23	C₃²	C₃²×A₄	1	13	yes	—
24	C₉	—	4	27	no	—
25	C₂×C₃	—	3	39	no	—
26	C₂×C₃	—	3	1	no	—
27	C₂²	C₃³×C₉	1	1	yes	characteristic, complemented, Sylow
28	C₃	C₃²×C₂²⋊C₉	1	39	yes	direct product factor
29	C₃	C₃³×A₄	1	1	yes	characteristic
30	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.