Subgroups — Dic₅₅₂₄ #36348374

Order 22096.

18 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₇₆₂	C₂	1	2	yes	maximal
2	C₈×C₁₃₈₁	C₂	1	1	yes	maximal, characteristic
3	C₄×C₁₃₈₁	C₂²	1	1	yes	characteristic
4	Dic₁₃₈₁	—	2	2	no	—
5	C₂×C₁₃₈₁	D₄	1	1	yes	characteristic
6	C₁₃₈₁	Q₁₆	1	1	yes	characteristic, complemented, Sylow
7	Q₁₆	—	1381	1	no	maximal, Sylow
8	Q₈	—	1381	2	no	—
9	C₈	D₁₃₈₁	1	1	yes	characteristic
10	C₄	—	2762	2	no	—
11	C₄	C₂×D₁₃₈₁	1	1	yes	characteristic
12	C₂	D₅₅₂₄	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
6. C₁₃₈₁	Q₁₆	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.