Subgroups — C₄×D₉ #608

Order 72.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₉	C₂	1	1	yes	maximal, characteristic
2	C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×D₃	—	3	1	no	maximal
5	C₂×C₉	C₂²	1	1	yes	characteristic
6	D₉	C₄	1	2	yes	direct product factor
7	C₂×D₃	—	3	1	no	—
8	C₃×C₄	D₃	1	1	yes	characteristic
9	Dic₃	—	3	1	no	—
10	C₉	C₂×C₄	1	1	yes	characteristic, complemented, Sylow
11	C₂×C₄	—	9	1	no	Sylow
12	C₂×C₃	C₂×D₃	1	1	yes	characteristic
13	D₃	—	3	2	no	—
14	C₂²	—	9	1	no	—
15	C₄	—	9	1	no	—
16	C₄	D₉	1	1	yes	characteristic, direct product factor
17	C₃	C₄×D₃	1	1	yes	characteristic
18	C₂	—	9	2	no	—
19	C₂	C₂×D₉	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.