Subgroups — #6875

Order 243.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂₇⋊C₃	C₃	1	2	yes	maximal
2	C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₉⋊C₉	C₃	1	1	yes	maximal, characteristic
4	C₃×C₉	—	3	1	no	—
5	C₃×C₉	C₃²	1	1	yes	characteristic
6	C₂₇	—	3	2	no	—
7	C₂₇	C₉	1	3	yes	complemented
8	C₃²	3₋¹⁺²	1	1	yes	characteristic
9	C₉	—	9	1	no	—
10	C₉	C₃×C₉	1	1	yes	characteristic
11	C₉	3₋¹⁺²	1	2	yes	—
12	C₃	—	3	1	no	—
13	C₃	C₉⋊C₉	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
7. C₂₇	C₉	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂₇⋊C₃	3
C₉⋊C₉	3