Subgroups — C₂×#157 #648

Order 72.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃⋊D₃	C₂	1	1	yes	maximal, characteristic
2	#157	C₂	1	2	yes	maximal, direct product factor
3	C₂×C₃²	C₄	1	1	yes	characteristic, complemented
4	C₃⋊D₃	C₄	1	1	yes	characteristic, complemented
5	C₃⋊D₃	C₂²	1	1	yes	characteristic
6	C₂×D₃	—	6	2	no	—
7	C₃²	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
8	C₂×C₄	—	9	1	no	maximal, Sylow
9	C₂×C₃	—	2	2	no	—
10	D₃	—	6	2	no	—
11	D₃	—	6	2	no	—
12	C₂²	—	9	1	no	—
13	C₄	—	9	2	no	—
14	C₃	—	2	2	no	—
15	C₂	—	9	1	no	—
16	C₂	—	9	1	no	—
17	C₂	#157	1	1	yes	characteristic, direct product factor

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.