Subgroups — C₃²×Dic₃ #1105

Order 108.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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