Subgroups — D₇₂ #3665

Order 144.

33 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₃₆	C₂	1	2	yes	maximal, complemented
2	C₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	D₂₄	—	3	1	no	maximal
4	C₂×D₉	—	2	2	no	—
5	C₄×C₉	C₂²	1	1	yes	characteristic
6	D₁₂	—	3	2	no	—
7	C₃×C₈	D₃	1	1	yes	characteristic
8	C₂×C₉	D₄	1	1	yes	characteristic
9	D₉	—	4	2	no	—
10	D₈	—	9	1	no	Sylow
11	C₂×D₃	—	6	2	no	—
12	C₃×C₄	C₂×D₃	1	1	yes	characteristic
13	C₉	D₈	1	1	yes	characteristic, complemented, Sylow
14	D₄	—	9	2	no	—
15	C₈	D₉	1	1	yes	characteristic, complemented
16	C₂×C₃	D₁₂	1	1	yes	characteristic
17	D₃	—	12	2	no	—
18	C₂²	—	18	2	no	—
19	C₄	C₂×D₉	1	1	yes	characteristic
20	C₃	D₂₄	1	1	yes	characteristic
21	C₂	—	36	2	no	—
22	C₂	D₃₆	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.