Subgroups — C₉×Dic₁₄ #92598

Order 504.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₇×C₉	C₂	1	1	yes	maximal, characteristic
2	C₉×Dic₇	C₂	1	2	yes	maximal
3	C₃×Dic₁₄	C₃	1	1	yes	maximal, characteristic
4	C₂×C₇×C₉	C₂²	1	1	yes	characteristic
5	C₃×C₄×C₇	C₂×C₃	1	1	yes	characteristic
6	C₃×Dic₇	C₂×C₃	1	2	yes	—
7	Q₈×C₉	—	7	1	no	maximal, Hall
8	C₇×C₉	Q₈	1	1	yes	characteristic, complemented, Hall
9	Dic₁₄	C₉	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₃×C₇	C₂²×C₃	1	1	yes	characteristic
11	C₄×C₉	—	7	2	no	—
12	C₄×C₉	D₇	1	1	yes	characteristic
13	C₄×C₇	C₂×C₉	1	1	yes	characteristic
14	Dic₇	C₂×C₉	1	2	yes	—
15	C₃×Q₈	—	7	1	no	—
16	C₃×C₇	C₃×Q₈	1	1	yes	characteristic
17	C₂×C₉	C₂×D₇	1	1	yes	characteristic
18	C₂×C₇	C₂²×C₉	1	1	yes	characteristic
19	C₃×C₄	—	7	2	no	—
20	C₃×C₄	C₃×D₇	1	1	yes	characteristic
21	C₉	Dic₁₄	1	1	yes	characteristic, direct product factor, Sylow
22	Q₈	—	7	1	no	Sylow
23	C₇	Q₈×C₉	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃	C₂×C₃×D₇	1	1	yes	characteristic
25	C₄	—	7	2	no	—
26	C₄	C₉×D₇	1	1	yes	characteristic
27	C₃	C₃×Dic₁₄	1	1	yes	characteristic
28	C₂	C₂×C₉×D₇	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.