Subgroups — C₃³×#11758603 #41008644

Order 26973.

1160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×#11758603	C₃	1	39	yes	maximal, direct product factor
2	C₃³×#66524	C₃	1	1	yes	maximal, characteristic
3	C₃×#11758603	C₃²	1	117	yes	direct product factor
4	C₃²×#66524	C₉	1	26	yes	—
5	C₃²×#66524	C₃²	1	13	yes	—
6	C₃⁴×C₃₇	C₉	1	1	yes	characteristic
7	C₃³×C₃₇	C₂₇	1	27	yes	complemented
8	C₃³×C₃₇	C₃×C₉	1	13	yes	—
9	C₃×#66524	C₃×C₉	1	104	yes	—
10	C₃×#66524	C₃³	1	13	yes	—
11	#11758603	C₃³	1	27	yes	direct product factor
12	C₃³×C₂₇	—	37	1	no	maximal, Sylow
13	C₃²×C₃₇	C₃×C₂₇	1	117	yes	complemented
14	C₃²×C₃₇	C₃²×C₉	1	13	yes	—
15	#66524	C₃²×C₉	1	26	yes	—
16	#66524	C₃⁴	1	1	yes	characteristic
17	C₃³×C₉	—	37	1	no	—
18	C₃²×C₂₇	—	37	39	no	—
19	C₃×C₃₇	C₃²×C₂₇	1	39	yes	complemented
20	C₃×C₃₇	C₃³×C₉	1	1	yes	characteristic
21	C₃⁴	#66526	1	1	yes	characteristic
22	C₃²×C₉	—	37	26	no	—
23	C₃²×C₉	—	37	13	no	—
24	C₃×C₂₇	—	37	117	no	—
25	C₃₇	C₃³×C₂₇	1	1	yes	characteristic, complemented, Sylow
26	C₃³	#11758603	1	27	yes	direct product factor
27	C₃³	C₃×#66526	1	13	yes	—
28	C₃×C₉	—	37	104	no	—
29	C₃×C₉	—	37	13	no	—
30	C₂₇	—	37	27	no	—
31	C₃²	C₃×#11758603	1	117	yes	direct product factor
32	C₃²	C₃²×#66526	1	13	yes	—
33	C₉	—	37	1	no	—
34	C₉	—	37	26	no	—
35	C₃	C₃²×#11758603	1	39	yes	direct product factor
36	C₃	C₃³×#66526	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.