Subgroups — #3701

Order 144.

60 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	D₃₆	C₂	1	3	yes	maximal, complemented
3	C₄×D₉	C₂	1	3	yes	maximal, complemented
4	#239	—	3	1	no	maximal
5	C₂×D₉	C₂²	1	3	yes	—
6	C₄×C₉	C₂²	1	3	yes	—
7	Dic₉	C₂²	1	1	yes	characteristic
8	C₃×Q₈	D₃	1	1	yes	characteristic
9	D₁₂	—	3	3	no	—
10	C₄×D₃	—	3	3	no	—
11	C₂×C₉	C₂³	1	1	yes	characteristic
12	D₉	—	2	3	no	—
13	#41	—	9	1	no	Sylow
14	C₂×D₃	—	3	3	no	—
15	C₃×C₄	C₂×D₃	1	3	yes	—
16	Dic₃	—	3	1	no	—
17	C₉	#41	1	1	yes	characteristic, complemented, Sylow
18	Q₈	D₉	1	1	yes	characteristic, complemented
19	D₄	—	9	3	no	—
20	C₂×C₄	—	9	3	no	—
21	C₂×C₃	C₂²×D₃	1	1	yes	characteristic
22	D₃	—	6	3	no	—
23	C₂²	—	9	3	no	—
24	C₄	—	9	1	no	—
25	C₄	C₂×D₉	1	3	yes	—
26	C₃	#239	1	1	yes	characteristic
27	C₂	—	18	3	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.