Subgroups — Dic₉₃₈₆ #72273607

Order 37544.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₇₂₂	—	13	1	no	maximal, Hall
2	Dic₄₆₉₃	C₂	1	2	yes	maximal
3	C₄×C₁₃×C₃₆₁	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₃×C₃₆₁	C₂²	1	1	yes	characteristic
5	C₁₃×C₃₆₁	Q₈	1	1	yes	characteristic, complemented, Hall
6	Dic₄₉₄	—	19	1	no	maximal
7	C₄×C₃₆₁	D₁₃	1	1	yes	characteristic
8	Dic₃₆₁	—	13	2	no	—
9	C₄×C₁₃×C₁₉	D₁₉	1	1	yes	characteristic
10	Dic₂₄₇	—	19	2	no	—
11	C₂×C₃₆₁	C₂×D₁₃	1	1	yes	characteristic
12	C₂×C₁₃×C₁₉	C₂×D₁₉	1	1	yes	characteristic
13	C₃₆₁	Dic₂₆	1	1	yes	characteristic, complemented, Sylow
14	C₁₃×C₁₉	Dic₃₈	1	1	yes	characteristic
15	Dic₃₈	—	247	1	no	—
16	Dic₂₆	—	361	1	no	Hall
17	C₄×C₁₉	D₂₄₇	1	1	yes	characteristic
18	Dic₁₉	—	247	2	no	—
19	C₄×C₁₃	D₃₆₁	1	1	yes	characteristic
20	Dic₁₃	—	361	2	no	—
21	C₂×C₁₉	C₂×D₂₄₇	1	1	yes	characteristic
22	C₂×C₁₃	C₂×D₃₆₁	1	1	yes	characteristic
23	C₁₉	Dic₄₉₄	1	1	yes	characteristic
24	C₁₃	Dic₇₂₂	1	1	yes	characteristic, complemented, Sylow
25	Q₈	—	4693	1	no	Sylow
26	C₄	—	4693	2	no	—
27	C₄	D₄₆₉₃	1	1	yes	characteristic
28	C₂	C₂×D₄₆₉₃	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.