Subgroups — C₃×#10588062 #13133665

Order 1701.

480 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×H(3,𝔽₃)	C₃	1	1	yes	maximal, characteristic
2	C₃×#4430	C₃	1	8	yes	maximal, complemented
3	C₃²×C₇⋊C₉	C₃	1	4	yes	maximal, complemented
4	#10588062	C₃	1	27	yes	maximal, direct product factor
5	C₃×#737	—	7	1	no	maximal, Sylow
6	C₃³×C₇	C₃²	1	4	yes	—
7	C₇×H(3,𝔽₃)	C₃²	1	9	yes	—
8	#4430	C₃²	1	72	yes	complemented
9	C₃×C₇⋊C₉	C₃²	1	1	yes	characteristic
10	C₃×C₇⋊C₉	C₃²	1	8	yes	—
11	C₃×C₇⋊C₉	C₃²	1	36	yes	complemented
12	#737	—	7	27	no	—
13	C₃×3₋¹⁺²	—	7	8	no	—
14	C₃×H(3,𝔽₃)	ΓL(1,𝔽₈)	1	1	yes	characteristic
15	C₃²×C₉	—	7	4	no	—
16	C₃²×C₇	—	3	12	no	—
17	C₃²×C₇	C₃³	1	12	yes	—
18	C₃²×C₇	C₃³	1	1	yes	characteristic
19	C₇⋊C₉	C₃³	1	3	yes	—
20	C₇⋊C₉	C₃³	1	24	yes	—
21	C₃³	C₃×ΓL(1,𝔽₈)	1	4	yes	—
22	3₋¹⁺²	—	7	72	no	—
23	H(3,𝔽₃)	C₃×ΓL(1,𝔽₈)	1	9	yes	—
24	C₃×C₉	—	7	36	no	—
25	C₃×C₉	—	7	1	no	—
26	C₃×C₉	—	7	8	no	—
27	C₃×C₇	—	3	12	no	—
28	C₃×C₇	#737	1	3	yes	complemented
29	C₃×C₇	C₃⁴	1	1	yes	characteristic
30	C₃²	—	3	12	no	—
31	C₃²	C₃²×ΓL(1,𝔽₈)	1	12	yes	—
32	C₃²	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
33	C₉	—	7	3	no	—
34	C₉	—	7	24	no	—
35	C₇	C₃×#737	1	1	yes	characteristic, complemented, Sylow
36	C₃	—	3	12	no	—
37	C₃	#10588062	1	3	yes	direct product factor
38	C₃	C₃³×ΓL(1,𝔽₈)	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.