Subgroups — #66353

Order 324.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₉	C₃	1	1	yes	maximal, characteristic
2	C₂²⋊C₂₇	C₃	1	3	yes	maximal, complemented
3	C₂₇⋊C₃	—	4	1	no	maximal, Sylow
4	C₂×C₃×C₉	—	3	1	no	—
5	C₂²×C₃²	C₉	1	1	yes	characteristic
6	C₂²×C₉	C₉	1	2	yes	—
7	C₂²×C₉	C₃²	1	1	yes	characteristic
8	C₃×C₉	A₄	1	1	yes	characteristic
9	C₂₇	—	4	3	no	—
10	C₂×C₃²	—	3	1	no	—
11	C₂×C₉	—	3	2	no	—
12	C₂×C₉	—	3	1	no	—
13	C₂²×C₃	—	3	1	no	—
14	C₂²×C₃	C₃×C₉	1	1	yes	characteristic
15	C₃²	C₂²⋊C₉	1	1	yes	characteristic
16	C₉	C₂²⋊C₉	1	2	yes	—
17	C₉	C₃×A₄	1	1	yes	characteristic
18	C₂×C₃	—	3	3	no	—
19	C₂×C₃	—	3	1	no	—
20	C₂²	C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₃	—	3	1	no	—
22	C₃	C₃×C₂²⋊C₉	1	1	yes	characteristic
23	C₂	—	3	1	no	—

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

N	H ≅ G/N	type
2. C₂²⋊C₂₇	C₃	semidirect
20. C₂²	C₂₇⋊C₃	semidirect

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