Subgroups — C₃×C₉×C₂₇ #10624678

Order 729.

202 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₂₇	C₃	1	3	yes	maximal
2	C₃×C₉²	C₃	1	1	yes	maximal, characteristic
3	C₉×C₂₇	C₃	1	9	yes	maximal, direct product factor
4	C₃²×C₉	C₉	1	3	yes	—
5	C₃²×C₉	C₃²	1	1	yes	characteristic
6	C₃×C₂₇	C₉	1	27	yes	direct product factor
7	C₃×C₂₇	C₃²	1	9	yes	—
8	C₉²	C₉	1	6	yes	—
9	C₉²	C₃²	1	3	yes	—
10	C₃³	C₃×C₉	1	1	yes	characteristic
11	C₃×C₉	C₂₇	1	27	yes	direct product factor
12	C₃×C₉	C₃×C₉	1	2	yes	—
13	C₃×C₉	C₃×C₉	1	9	yes	—
14	C₃×C₉	C₃×C₉	1	9	yes	—
15	C₃×C₉	C₃³	1	1	yes	characteristic
16	C₂₇	C₃×C₉	1	27	yes	direct product factor
17	C₃²	C₉²	1	3	yes	—
18	C₃²	C₃×C₂₇	1	9	yes	—
19	C₃²	C₃²×C₉	1	1	yes	characteristic
20	C₉	C₉²	1	6	yes	—
21	C₉	C₃×C₂₇	1	27	yes	direct product factor
22	C₉	C₃²×C₉	1	3	yes	—
23	C₃	C₉×C₂₇	1	9	yes	direct product factor
24	C₃	C₃×C₉²	1	1	yes	characteristic
25	C₃	C₃²×C₂₇	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.