Subgroups — C₂₇×#11758603 #41008264

Order 26973.

152 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#11758603	C₃	1	3	yes	maximal
2	C₂₇×#66524	C₃	1	1	yes	maximal, characteristic
3	C₃×#11758603	C₉	1	9	yes	—
4	C₃×#11758601	C₉	1	2	yes	—
5	C₉×#66524	C₃²	1	1	yes	characteristic
6	C₃×C₂₇×C₃₇	C₉	1	1	yes	characteristic
7	C₃×C₉×C₃₇	C₃×C₉	1	1	yes	characteristic
8	C₃×#66524	C₃×C₉	1	3	yes	—
9	#11758603	C₂₇	1	27	yes	direct product factor
10	C₂₇×C₃₇	C₂₇	1	3	yes	complemented
11	#11758601	C₂₇	1	6	yes	complemented
12	C₂₇²	—	37	1	no	maximal, Sylow
13	C₃²×C₃₇	C₉²	1	1	yes	characteristic
14	C₉×C₃₇	C₃×C₂₇	1	1	yes	characteristic
15	C₉×C₃₇	C₃×C₂₇	1	2	yes	—
16	#66524	C₃×C₂₇	1	9	yes	—
17	C₉×C₂₇	—	37	3	no	—
18	C₉×C₂₇	—	37	1	no	—
19	C₃×C₃₇	C₉×C₂₇	1	3	yes	—
20	C₃×C₃₇	C₉×C₂₇	1	1	yes	characteristic
21	C₃×C₂₇	—	37	9	no	—
22	C₃×C₂₇	—	37	2	no	—
23	C₃×C₂₇	#66526	1	1	yes	characteristic
24	C₉²	—	37	1	no	—
25	C₃₇	C₂₇²	1	1	yes	characteristic, complemented, Sylow
26	C₃×C₉	—	37	3	no	—
27	C₃×C₉	C₃×#66526	1	1	yes	characteristic
28	C₂₇	—	37	27	no	—
29	C₂₇	—	37	6	no	—
30	C₂₇	#11758603	1	3	yes	direct product factor
31	C₃²	C₉×#66526	1	1	yes	characteristic
32	C₉	—	37	9	no	—
33	C₉	C₃×#11758603	1	1	yes	characteristic
34	C₉	(C₃₇⋊C₃)⋊C₂₇	1	2	yes	—
35	C₃	C₂₇×#66526	1	3	yes	—
36	C₃	C₉×#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.