Subgroups — C₃×#11760452 #15691691

Order 3159.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11760452	C₃	1	27	yes	maximal, direct product factor
2	C₃×#66851	C₃	1	8	yes	maximal, complemented
3	C₃²×C₁₃⋊C₉	C₃	1	4	yes	maximal, complemented
4	C₃×C₁₃×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
5	C₃³×C₁₃	C₃²	1	4	yes	—
6	C₁₃×H(3,𝔽₃)	C₃²	1	9	yes	—
7	#66851	C₃²	1	72	yes	complemented
8	C₃×C₁₃⋊C₉	C₃²	1	1	yes	characteristic
9	C₃×C₁₃⋊C₉	C₃²	1	8	yes	—
10	C₃×C₁₃⋊C₉	C₃²	1	36	yes	complemented
11	C₃×#737	—	13	1	no	maximal, Sylow
12	C₃²×C₁₃	—	3	12	no	—
13	C₃²×C₁₃	C₃³	1	12	yes	—
14	C₃²×C₁₃	C₃³	1	1	yes	characteristic
15	C₁₃⋊C₉	C₃³	1	3	yes	—
16	C₁₃⋊C₉	C₃³	1	24	yes	—
17	#737	—	13	27	no	—
18	C₃×3₋¹⁺²	—	13	8	no	—
19	C₃×H(3,𝔽₃)	C₁₃⋊C₃	1	1	yes	characteristic
20	C₃²×C₉	—	13	4	no	—
21	C₃×C₁₃	—	3	12	no	—
22	C₃×C₁₃	#737	1	3	yes	complemented
23	C₃×C₁₃	C₃⁴	1	1	yes	characteristic
24	C₃³	C₃×C₁₃⋊C₃	1	4	yes	—
25	3₋¹⁺²	—	13	72	no	—
26	H(3,𝔽₃)	C₃×C₁₃⋊C₃	1	9	yes	—
27	C₃×C₉	—	13	36	no	—
28	C₃×C₉	—	13	1	no	—
29	C₃×C₉	—	13	8	no	—
30	C₁₃	C₃×#737	1	1	yes	characteristic, complemented, Sylow
31	C₃²	—	3	12	no	—
32	C₃²	C₃²×C₁₃⋊C₃	1	12	yes	—
33	C₃²	C₃²×C₁₃⋊C₃	1	1	yes	characteristic
34	C₉	—	13	3	no	—
35	C₉	—	13	24	no	—
36	C₃	—	3	12	no	—
37	C₃	#11760452	1	3	yes	direct product factor
38	C₃	C₃³×C₁₃⋊C₃	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.