Subgroups — C₉×D₈ #3682

Order 144.

33 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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