Subgroups — C₃³×Dic₃ #66463

Order 324.

324 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⁴	C₂	1	1	yes	maximal, characteristic
2	C₃³×C₄	—	3	1	no	maximal
3	C₃²×Dic₃	C₃	1	13	yes	maximal, direct product factor
4	C₃⁴	C₄	1	1	yes	characteristic, complemented, Sylow
5	C₂×C₃³	—	2	13	no	—
6	C₂×C₃³	D₃	1	1	yes	characteristic
7	C₂×C₃³	C₂×C₃	1	13	yes	—
8	C₃²×C₄	—	3	13	no	—
9	C₃×Dic₃	C₃²	1	13	yes	direct product factor
10	C₃³	—	2	13	no	—
11	C₃³	Dic₃	1	1	yes	characteristic, direct product factor
12	C₃³	C₃×C₄	1	13	yes	complemented
13	C₂×C₃²	—	2	52	no	—
14	C₂×C₃²	C₃×D₃	1	13	yes	—
15	C₂×C₃²	C₂×C₃²	1	13	yes	—
16	C₃×C₄	—	3	13	no	—
17	Dic₃	C₃³	1	1	yes	characteristic, direct product factor
18	C₃²	—	2	52	no	—
19	C₃²	C₃×Dic₃	1	13	yes	direct product factor
20	C₃²	C₃²×C₄	1	13	yes	complemented
21	C₂×C₃	—	2	13	no	—
22	C₂×C₃	C₃²×D₃	1	13	yes	—
23	C₂×C₃	C₂×C₃³	1	1	yes	characteristic
24	C₄	—	3	1	no	Sylow
25	C₃	—	2	13	no	—
26	C₃	C₃²×Dic₃	1	13	yes	direct product factor
27	C₃	C₃³×C₄	1	1	yes	characteristic, complemented
28	C₂	C₃³×D₃	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.