Subgroups — Q₈×D₉ #3700

Order 144.

57 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₉	C₂	1	3	yes	maximal
3	Dic₁₈	C₂	1	3	yes	maximal, complemented
4	D₃×Q₈	—	3	1	no	maximal
5	C₂×D₉	C₂²	1	1	yes	characteristic
6	C₄×C₉	C₂²	1	3	yes	—
7	Dic₉	C₂²	1	3	yes	—
8	C₃×Q₈	D₃	1	1	yes	characteristic
9	C₄×D₃	—	3	3	no	—
10	Dic₆	—	3	3	no	—
11	C₂×C₉	C₂³	1	1	yes	characteristic
12	D₉	Q₈	1	2	yes	direct product factor
13	C₂×Q₈	—	9	1	no	Sylow
14	C₂×D₃	—	3	1	no	—
15	C₃×C₄	C₂×D₃	1	3	yes	—
16	Dic₃	—	3	3	no	—
17	C₉	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
18	Q₈	—	9	3	no	—
19	Q₈	D₉	1	1	yes	characteristic, direct product factor
20	C₂×C₄	—	9	3	no	—
21	C₂×C₃	C₂²×D₃	1	1	yes	characteristic
22	D₃	—	3	2	no	—
23	C₂²	—	9	1	no	—
24	C₄	—	9	3	no	—
25	C₄	C₂×D₉	1	3	yes	—
26	C₃	D₃×Q₈	1	1	yes	characteristic
27	C₂	—	9	2	no	—
28	C₂	C₂²×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.