Subgroups — C₃×#23779834 #44525007

Order 30861.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11765917	C₃	1	3	yes	maximal
2	#23779834	C₃	1	9	yes	maximal, direct product factor
3	C₃²×C₉×C₁₂₇	C₃	1	1	yes	maximal, characteristic
4	C₃×#11765917	—	3	9	no	—
5	C₃×#11765917	C₃²	1	9	yes	—
6	C₃³×C₁₂₇	C₃²	1	1	yes	characteristic
7	C₃×C₉×C₁₂₇	C₉	1	9	yes	complemented
8	C₃×C₉×C₁₂₇	C₃²	1	3	yes	—
9	C₃²×C₁₂₇	C₃×C₉	1	3	yes	—
10	C₃²×C₁₂₇	3₋¹⁺²	1	9	yes	—
11	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
12	C₉×C₁₂₇	C₃×C₉	1	9	yes	complemented
13	#11765917	—	3	9	no	—
14	C₃×C₁₂₇	C₉⋊C₉	1	9	yes	complemented
15	C₃×C₁₂₇	C₃²×C₉	1	1	yes	characteristic
16	C₃×C₁₂₇	C₃×3₋¹⁺²	1	3	yes	—
17	C₃×C₉⋊C₉	—	127	1	no	maximal, Sylow
18	C₁₂₇	C₃×C₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
19	C₃²×C₉	—	127	3	no	—
20	C₃²×C₉	C₁₂₇⋊C₃	1	1	yes	characteristic
21	C₉⋊C₉	—	127	9	no	—
22	C₃³	C₃×C₁₂₇⋊C₃	1	1	yes	characteristic
23	C₃×C₉	—	381	9	no	—
24	C₃×C₉	—	127	9	no	—
25	C₃×C₉	#11765917	1	9	yes	complemented
26	C₃×C₉	C₃×C₁₂₇⋊C₃	1	3	yes	—
27	C₃²	C₃×#11765917	1	3	yes	—
28	C₃²	#16812183	1	9	yes	—
29	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
30	C₉	—	381	9	no	—
31	C₉	C₃×#11765917	1	9	yes	complemented
32	C₃	#23779834	1	9	yes	direct product factor
33	C₃	C₃²×#11765917	1	1	yes	characteristic
34	C₃	C₃×#16812183	1	3	yes	—

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.