Subgroups — H(3,𝔽₃)×#11765917 #44525015

Order 30861.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11765917	C₃	1	4	yes	maximal, complemented
2	C₃²⋊#11765917	C₃	1	8	yes	maximal, complemented
3	C₃×H(3,𝔽₃)×C₁₂₇	C₃	1	1	yes	maximal, characteristic
4	C₃×#11765917	—	3	12	no	—
5	C₃×#11765917	C₃²	1	8	yes	—
6	C₃×#11765917	C₃²	1	1	yes	characteristic
7	C₃³×C₁₂₇	C₃²	1	4	yes	—
8	H(3,𝔽₃)×C₁₂₇	C₉	1	9	yes	complemented
9	C₃²×C₁₂₇	—	3	4	no	—
10	C₃²×C₁₂₇	—	3	8	no	—
11	C₃²×C₁₂₇	C₃×C₉	1	12	yes	complemented
12	C₃²×C₁₂₇	C₃³	1	1	yes	characteristic
13	#11765917	—	3	8	no	—
14	#11765917	H(3,𝔽₃)	1	3	yes	direct product factor
15	C₃×C₁₂₇	—	3	12	no	—
16	C₃×C₁₂₇	C₃²×C₉	1	1	yes	characteristic
17	C₃×C₁₂₇	C₃×H(3,𝔽₃)	1	1	yes	characteristic
18	C₃×C₁₂₇	#737	1	2	yes	—
19	C₉×H(3,𝔽₃)	—	127	1	no	maximal, Sylow
20	C₁₂₇	C₉×H(3,𝔽₃)	1	1	yes	characteristic, complemented, Sylow
21	C₃×H(3,𝔽₃)	C₁₂₇⋊C₃	1	1	yes	characteristic
22	C₃²×C₉	—	127	4	no	—
23	C₃²⋊C₉	—	127	8	no	—
24	C₃³	C₃×C₁₂₇⋊C₃	1	4	yes	—
25	H(3,𝔽₃)	#11765917	1	9	yes	direct product factor
26	C₃×C₉	—	381	12	no	—
27	C₃×C₉	—	127	8	no	—
28	C₃×C₉	—	127	1	no	—
29	C₃²	—	3	4	no	—
30	C₃²	—	3	8	no	—
31	C₃²	C₃×#11765917	1	12	yes	complemented
32	C₃²	C₃²×C₁₂₇⋊C₃	1	1	yes	characteristic
33	C₉	—	381	8	no	—
34	C₉	—	127	3	no	—
35	C₃	—	3	12	no	—
36	C₃	C₃²×#11765917	1	1	yes	characteristic
37	C₃	H(3,𝔽₃)×C₁₂₇⋊C₃	1	1	yes	characteristic
38	C₃	#23779859	1	2	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.