Subgroups — C₃²×#15688534 #41008624

Order 26973.

188 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#15688534	C₃	1	12	yes	maximal, direct product factor
2	C₃²×#11758601	C₃	1	1	yes	maximal, characteristic
3	#15688534	C₃²	1	9	yes	direct product factor
4	C₃×#11758601	C₉	1	8	yes	—
5	C₃×#11758601	C₃²	1	4	yes	—
6	C₃²×C₉×C₃₇	C₉	1	1	yes	characteristic
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	#11758601	C₃×C₉	1	8	yes	—
11	#11758601	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	—	37	1	no	—
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	#66526	1	1	yes	characteristic
22	C₃×C₂₇	—	37	8	no	—
23	C₃×C₂₇	—	37	4	no	—
24	C₈₁	—	37	9	no	—
25	C₃₇	C₃²×C₈₁	1	1	yes	characteristic, complemented, Sylow
26	C₃³	#11758603	1	1	yes	characteristic
27	C₃×C₉	#11758603	1	8	yes	—
28	C₃×C₉	C₃×#66526	1	4	yes	—
29	C₂₇	—	37	8	no	—
30	C₂₇	—	37	1	no	—
31	C₃²	#15688534	1	9	yes	direct product factor
32	C₃²	C₃×#11758603	1	4	yes	—
33	C₉	C₃×#11758603	1	8	yes	—
34	C₉	C₃²×#66526	1	1	yes	characteristic
35	C₃	C₃×#15688534	1	12	yes	direct product factor
36	C₃	C₃²×#11758603	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.