Subgroups — C₃²×C₂²⋊C₉ #66441

Order 324.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃³	C₃	1	1	yes	maximal, characteristic
2	C₃×C₂²⋊C₉	C₃	1	12	yes	maximal, direct product factor
3	C₃²×C₉	—	4	1	no	maximal, Sylow
4	C₂×C₃³	—	3	1	no	—
5	C₂²×C₃²	C₉	1	9	yes	complemented
6	C₂²×C₃²	C₃²	1	4	yes	—
7	C₂²⋊C₉	C₃²	1	9	yes	direct product factor
8	C₃³	A₄	1	1	yes	characteristic
9	C₃×C₉	—	4	12	no	—
10	C₂×C₃²	—	3	9	no	—
11	C₂×C₃²	—	3	4	no	—
12	C₂²×C₃	C₃×C₉	1	12	yes	complemented
13	C₂²×C₃	C₃³	1	1	yes	characteristic
14	C₃²	C₂²⋊C₉	1	9	yes	direct product factor
15	C₃²	C₃×A₄	1	4	yes	—
16	C₉	—	4	9	no	—
17	C₂×C₃	—	3	12	no	—
18	C₂×C₃	—	3	1	no	—
19	C₂²	C₃²×C₉	1	1	yes	characteristic, complemented, Sylow
20	C₃	C₃×C₂²⋊C₉	1	12	yes	direct product factor
21	C₃	C₃²×A₄	1	1	yes	characteristic
22	C₂	—	3	1	no	—

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.