Subgroups — D₃₆ #609

Order 72.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₉	C₂	1	2	yes	maximal, complemented
2	C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₁₂	—	3	1	no	maximal
4	C₂×C₉	C₂²	1	1	yes	characteristic
5	D₉	—	2	2	no	—
6	C₂×D₃	—	3	2	no	—
7	C₃×C₄	D₃	1	1	yes	characteristic
8	C₉	D₄	1	1	yes	characteristic, complemented, Sylow
9	D₄	—	9	1	no	Sylow
10	C₂×C₃	C₂×D₃	1	1	yes	characteristic
11	D₃	—	6	2	no	—
12	C₂²	—	9	2	no	—
13	C₄	D₉	1	1	yes	characteristic, complemented
14	C₃	D₁₂	1	1	yes	characteristic
15	C₂	—	18	2	no	—
16	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.