Subgroups — #92586

Order 504.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₆₃	C₂	1	1	yes	maximal, characteristic
2	C₉×Dic₇	C₂	1	1	yes	maximal, characteristic
3	C₇×Dic₉	C₂	1	1	yes	maximal, characteristic
4	#4248	—	3	1	no	maximal
5	C₂×C₇×C₉	C₂²	1	1	yes	characteristic
6	Dic₂₁	—	3	1	no	—
7	C₃×Dic₇	D₃	1	1	yes	characteristic
8	C₇×Dic₃	—	3	1	no	—
9	Dic₁₈	—	7	1	no	maximal, Hall
10	C₇×C₉	Q₈	1	1	yes	characteristic, complemented, Hall
11	Dic₁₄	—	9	1	no	Hall
12	C₂×C₃×C₇	C₂×D₃	1	1	yes	characteristic
13	C₄×C₉	—	7	1	no	—
14	Dic₉	—	7	1	no	—
15	Dic₉	D₇	1	1	yes	characteristic
16	C₄×C₇	—	9	1	no	—
17	Dic₇	—	9	1	no	—
18	Dic₇	D₉	1	1	yes	characteristic
19	Dic₆	—	21	1	no	—
20	C₃×C₇	Dic₆	1	1	yes	characteristic
21	C₂×C₉	C₂×D₇	1	1	yes	characteristic
22	C₂×C₇	C₂×D₉	1	1	yes	characteristic
23	C₃×C₄	—	7	1	no	—
24	Dic₃	—	3	1	no	—
25	Dic₃	—	21	1	no	—
26	C₉	Dic₁₄	1	1	yes	characteristic, complemented, Sylow
27	Q₈	—	63	1	no	Sylow
28	C₇	Dic₁₈	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	D₃×D₇	1	1	yes	characteristic
30	C₄	—	7	1	no	—
31	C₄	—	9	1	no	—
32	C₄	—	63	1	no	—
33	C₃	#4248	1	1	yes	characteristic
34	C₂	D₇×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.