Subgroups — #88521

Order 432.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#6226	C₂	1	2	yes	maximal
2	C₃×C₈×C₉	C₂	1	1	yes	maximal, characteristic
3	#3746	—	3	1	no	maximal
4	Dic₃₆	—	3	3	no	maximal
5	C₃×C₄×C₉	C₂²	1	1	yes	characteristic
6	C₃⋊Dic₉	—	2	2	no	—
7	#634	—	3	2	no	—
8	C₃²×C₈	D₃	1	1	yes	characteristic
9	Dic₁₈	—	3	6	no	—
10	C₈×C₉	D₃	1	3	yes	—
11	C₂×C₃×C₉	D₄	1	1	yes	characteristic
12	Dic₁₂	—	9	3	no	—
13	Dic₁₂	—	9	1	no	—
14	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
15	C₃⋊Dic₃	—	6	2	no	—
16	C₄×C₉	C₂×D₃	1	3	yes	—
17	Dic₉	—	6	6	no	—
18	C₃×C₉	Q₁₆	1	1	yes	characteristic, complemented, Sylow
19	Dic₆	—	9	6	no	—
20	Dic₆	—	9	2	no	—
21	C₃×C₈	D₉	1	3	yes	—
22	C₃×C₈	C₃⋊D₃	1	1	yes	characteristic
23	C₂×C₃²	D₁₂	1	1	yes	characteristic
24	C₂×C₉	D₁₂	1	3	yes	—
25	Q₁₆	—	27	1	no	Sylow
26	C₃×C₄	C₂×D₉	1	3	yes	—
27	C₃×C₄	C₂×C₃⋊D₃	1	1	yes	characteristic
28	Dic₃	—	18	6	no	—
29	Dic₃	—	18	2	no	—
30	C₃²	Dic₁₂	1	1	yes	characteristic
31	C₉	Dic₁₂	1	3	yes	complemented
32	Q₈	—	27	2	no	—
33	C₈	C₃⋊D₉	1	1	yes	characteristic
34	C₂×C₃	D₃₆	1	3	yes	—
35	C₂×C₃	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
36	C₄	—	54	2	no	—
37	C₄	C₂×C₃⋊D₉	1	1	yes	characteristic
38	C₃	Dic₃₆	1	3	yes	complemented
39	C₃	#3746	1	1	yes	characteristic
40	C₂	C₄⋊(C₃⋊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.