Subgroups — C₃²×#15688500 #41007311

Order 26973.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688500	C₃	1	12	yes	maximal, direct product factor
2	C₃²×C₂₇×C₃₇	C₃	1	1	yes	maximal, characteristic
3	#15688500	C₃²	1	9	yes	direct product factor
4	C₃²×C₉×C₃₇	C₉	1	1	yes	characteristic
5	C₃×C₂₇×C₃₇	C₉	1	8	yes	—
6	C₃×C₂₇×C₃₇	C₃²	1	4	yes	—
7	C₃³×C₃₇	C₂₇	1	1	yes	characteristic
8	C₃×C₉×C₃₇	C₂₇	1	8	yes	—
9	C₃×C₉×C₃₇	C₃×C₉	1	4	yes	—
10	C₂₇×C₃₇	C₃×C₉	1	8	yes	—
11	C₂₇×C₃₇	C₃³	1	1	yes	characteristic
12	C₃²×C₈₁	—	37	1	no	maximal, Sylow
13	C₃²×C₃₇	C₈₁	1	9	yes	complemented
14	C₃²×C₃₇	C₃×C₂₇	1	4	yes	—
15	C₉×C₃₇	C₃×C₂₇	1	8	yes	—
16	C₉×C₃₇	C₃²×C₉	1	1	yes	characteristic
17	C₃²×C₂₇	C₃₇⋊C₃	1	1	yes	characteristic
18	C₃×C₈₁	—	37	12	no	—
19	C₃×C₃₇	C₃×C₈₁	1	12	yes	complemented
20	C₃×C₃₇	C₃²×C₂₇	1	1	yes	characteristic
21	C₃²×C₉	#66524	1	1	yes	characteristic
22	C₃×C₂₇	#66524	1	8	yes	—
23	C₃×C₂₇	C₃×C₃₇⋊C₃	1	4	yes	—
24	C₈₁	—	37	9	no	—
25	C₃₇	C₃²×C₈₁	1	1	yes	characteristic, complemented, Sylow
26	C₃³	#11758601	1	1	yes	characteristic
27	C₃×C₉	#11758601	1	8	yes	—
28	C₃×C₉	C₃×#66524	1	4	yes	—
29	C₂₇	C₃×#66524	1	8	yes	—
30	C₂₇	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
31	C₃²	#15688500	1	9	yes	direct product factor
32	C₃²	C₃×#11758601	1	4	yes	—
33	C₉	C₃×#11758601	1	8	yes	—
34	C₉	C₃²×#66524	1	1	yes	characteristic
35	C₃	C₃×#15688500	1	12	yes	direct product factor
36	C₃	C₃²×#11758601	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.