Subgroups — C₃×#157 #1109

Order 108.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	#157	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃³	C₄	1	1	yes	characteristic, complemented, Sylow
4	C₃⋊D₃	C₂×C₃	1	1	yes	characteristic
5	C₃×D₃	—	6	2	no	—
6	C₃×C₄	—	9	1	no	maximal
7	C₃²	—	2	2	no	—
8	C₃²	—	4	2	no	—
9	C₃²	C₃×C₄	1	1	yes	characteristic, complemented
10	C₂×C₃	—	9	1	no	—
11	D₃	—	6	2	no	—
12	C₄	—	9	1	no	Sylow
13	C₃	—	2	2	no	—
14	C₃	—	4	2	no	—
15	C₃	#157	1	1	yes	characteristic, direct product factor
16	C₂	—	9	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.