Subgroups — C₃²×#4430 #13133663

Order 1701.

576 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⁴×C₇	C₃	1	1	yes	maximal, characteristic
2	C₃×#4430	C₃	1	36	yes	maximal, direct product factor
3	C₃²×C₇⋊C₉	C₃	1	3	yes	maximal, complemented
4	C₃²×3₋¹⁺²	—	7	1	no	maximal, Sylow
5	C₃³×C₇	—	3	9	no	—
6	C₃³×C₇	C₃²	1	12	yes	—
7	C₃³×C₇	C₃²	1	1	yes	characteristic
8	#4430	C₃²	1	81	yes	direct product factor
9	C₃×C₇⋊C₉	C₃²	1	36	yes	complemented
10	C₃⁴	ΓL(1,𝔽₈)	1	1	yes	characteristic
11	C₃×3₋¹⁺²	—	7	36	no	—
12	C₃²×C₉	—	7	3	no	—
13	C₃²×C₇	—	3	36	no	—
14	C₃²×C₇	3₋¹⁺²	1	9	yes	complemented
15	C₃²×C₇	C₃³	1	9	yes	—
16	C₃²×C₇	C₃³	1	4	yes	—
17	C₇⋊C₉	C₃³	1	27	yes	complemented
18	C₃³	—	3	9	no	—
19	C₃³	C₃×ΓL(1,𝔽₈)	1	12	yes	—
20	C₃³	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
21	3₋¹⁺²	—	7	81	no	—
22	C₃×C₉	—	7	36	no	—
23	C₃×C₇	—	3	9	no	—
24	C₃×C₇	C₃×3₋¹⁺²	1	12	yes	complemented
25	C₃×C₇	C₃⁴	1	1	yes	characteristic
26	C₃²	—	3	36	no	—
27	C₃²	#4430	1	9	yes	direct product factor
28	C₃²	C₃²×ΓL(1,𝔽₈)	1	9	yes	—
29	C₃²	C₃²×ΓL(1,𝔽₈)	1	4	yes	—
30	C₉	—	7	27	no	—
31	C₇	C₃²×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
32	C₃	—	3	9	no	—
33	C₃	C₃×#4430	1	12	yes	direct product factor
34	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.