Subgroups — Dic₁₄⋊C₉ #92581

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	Dic₇⋊C₉	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, complemented, Hall
10	C₂×C₃×C₇	C₂²×C₃	1	1	yes	characteristic
11	C₄×C₉	—	7	2	no	—
12	C₄×C₉	—	7	1	no	—
13	C₄×C₇	C₂×C₉	1	1	yes	characteristic
14	Dic₇	C₂×C₉	1	2	yes	—
15	C₃×Q₈	—	21	1	no	—
16	C₃×C₇	C₃×Q₈	1	1	yes	characteristic
17	C₂×C₉	—	7	1	no	—
18	C₂×C₇	C₂²×C₉	1	1	yes	characteristic
19	C₃×C₄	—	7	2	no	—
20	C₃×C₄	AGL(1,𝔽₇)	1	1	yes	characteristic
21	C₉	—	7	1	no	Sylow
22	Q₈	—	21	1	no	Sylow
23	C₇	Q₈×C₉	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
25	C₄	—	7	2	no	—
26	C₄	D₇⋊C₉	1	1	yes	characteristic
27	C₃	ΓL(1,𝔽₈)⋊Q₈	1	1	yes	characteristic
28	C₂	C₂×D₇⋊C₉	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.