Subgroups — C₃×#10588036 #13133526

Order 1701.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇×C₉	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₇⋊C₉	C₃	1	3	yes	maximal
3	#10588036	C₃	1	9	yes	maximal, direct product factor
4	C₃×C₉⋊C₉	—	7	1	no	maximal, Sylow
5	C₃³×C₇	C₃²	1	1	yes	characteristic
6	C₃×C₇×C₉	C₉	1	9	yes	complemented
7	C₃×C₇×C₉	C₃²	1	3	yes	—
8	C₃×C₇⋊C₉	—	3	9	no	—
9	C₃×C₇⋊C₉	C₃²	1	9	yes	—
10	C₃²×C₉	—	7	3	no	—
11	C₃²×C₉	ΓL(1,𝔽₈)	1	1	yes	characteristic
12	C₉⋊C₉	—	7	9	no	—
13	C₃²×C₇	C₃×C₉	1	3	yes	—
14	C₃²×C₇	3₋¹⁺²	1	9	yes	—
15	C₃²×C₇	C₃³	1	1	yes	characteristic
16	C₇×C₉	C₃×C₉	1	9	yes	complemented
17	C₇⋊C₉	—	3	9	no	—
18	C₃³	C₃×ΓL(1,𝔽₈)	1	1	yes	characteristic
19	C₃×C₉	—	7	9	no	—
20	C₃×C₉	—	21	9	no	—
21	C₃×C₉	C₇⋊C₉	1	9	yes	complemented
22	C₃×C₉	C₃×ΓL(1,𝔽₈)	1	3	yes	—
23	C₃×C₇	C₉⋊C₉	1	9	yes	complemented
24	C₃×C₇	C₃²×C₉	1	1	yes	characteristic
25	C₃×C₇	C₃×3₋¹⁺²	1	3	yes	—
26	C₃²	#4428	1	9	yes	—
27	C₃²	C₃×C₇⋊C₉	1	3	yes	—
28	C₃²	C₃²×ΓL(1,𝔽₈)	1	1	yes	characteristic
29	C₉	—	21	9	no	—
30	C₉	C₃×C₇⋊C₉	1	9	yes	complemented
31	C₇	C₃×C₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
32	C₃	#10588036	1	9	yes	direct product factor
33	C₃	C₃×#4428	1	3	yes	—
34	C₃	C₃²×C₇⋊C₉	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.