Subgroups — C₃×C₂₇⋊C₃ #6902

Order 243.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₉	C₃	1	1	yes	maximal, characteristic
2	C₂₇⋊C₃	C₃	1	9	yes	maximal, direct product factor
3	C₃×C₂₇	C₃	1	3	yes	maximal, complemented
4	C₃³	C₉	1	1	yes	characteristic
5	C₃×C₉	C₉	1	2	yes	—
6	C₃×C₉	C₉	1	6	yes	—
7	C₃×C₉	C₃²	1	3	yes	—
8	C₃×C₉	C₃²	1	1	yes	characteristic
9	C₂₇	C₃²	1	9	yes	complemented
10	C₃²	—	3	3	no	—
11	C₃²	C₃×C₉	1	3	yes	—
12	C₃²	C₃×C₉	1	1	yes	characteristic
13	C₉	C₃×C₉	1	6	yes	—
14	C₉	C₃×C₉	1	2	yes	—
15	C₉	C₃³	1	1	yes	characteristic
16	C₃	—	3	3	no	—
17	C₃	C₂₇⋊C₃	1	3	yes	direct product factor
18	C₃	C₃²×C₉	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.