Subgroups — C₃×#26014604 #46798538

Order 33777.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₁₃₉⋊C₉	C₃	1	3	yes	maximal
2	#26014604	C₃	1	9	yes	maximal, direct product factor
3	C₃²×C₉×C₁₃₉	C₃	1	1	yes	maximal, characteristic
4	C₃×C₁₃₉⋊C₉	—	3	9	no	—
5	C₃×C₁₃₉⋊C₉	C₃²	1	9	yes	—
6	C₃³×C₁₃₉	C₃²	1	1	yes	characteristic
7	C₃×C₉×C₁₃₉	C₉	1	9	yes	complemented
8	C₃×C₉×C₁₃₉	C₃²	1	3	yes	—
9	C₃²×C₁₃₉	C₃×C₉	1	3	yes	—
10	C₃²×C₁₃₉	3₋¹⁺²	1	9	yes	—
11	C₃²×C₁₃₉	C₃³	1	1	yes	characteristic
12	C₉×C₁₃₉	C₃×C₉	1	9	yes	complemented
13	C₁₃₉⋊C₉	—	3	9	no	—
14	C₃×C₁₃₉	C₉⋊C₉	1	9	yes	complemented
15	C₃×C₁₃₉	C₃²×C₉	1	1	yes	characteristic
16	C₃×C₁₃₉	C₃×3₋¹⁺²	1	3	yes	—
17	C₃×C₉⋊C₉	—	139	1	no	maximal, Sylow
18	C₁₃₉	C₃×C₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
19	C₃²×C₉	—	139	3	no	—
20	C₃²×C₉	C₁₃₉⋊C₃	1	1	yes	characteristic
21	C₉⋊C₉	—	139	9	no	—
22	C₃³	C₃×C₁₃₉⋊C₃	1	1	yes	characteristic
23	C₃×C₉	—	139	9	no	—
24	C₃×C₉	—	417	9	no	—
25	C₃×C₉	C₁₃₉⋊C₉	1	9	yes	complemented
26	C₃×C₉	C₃×C₁₃₉⋊C₃	1	3	yes	—
27	C₃²	C₃×C₁₃₉⋊C₉	1	3	yes	—
28	C₃²	#16836728	1	9	yes	—
29	C₃²	C₃²×C₁₃₉⋊C₃	1	1	yes	characteristic
30	C₉	—	417	9	no	—
31	C₉	C₃×C₁₃₉⋊C₉	1	9	yes	complemented
32	C₃	#26014604	1	9	yes	direct product factor
33	C₃	C₃²×C₁₃₉⋊C₉	1	1	yes	characteristic
34	C₃	C₃×#16836728	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.