Subgroups — Dic₄₃₉₄ #72215839

Order 17576.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₁₉₇	C₂	1	2	yes	maximal
2	C₄×C₂₁₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂₁₉₇	C₂²	1	1	yes	characteristic
4	C₂₁₉₇	Q₈	1	1	yes	characteristic, complemented, Sylow
5	Dic₃₃₈	—	13	1	no	maximal
6	C₄×C₁₆₉	D₁₃	1	1	yes	characteristic
7	Dic₁₆₉	—	13	2	no	—
8	C₂×C₁₆₉	C₂×D₁₃	1	1	yes	characteristic
9	C₁₆₉	Dic₂₆	1	1	yes	characteristic
10	Dic₂₆	—	169	1	no	—
11	C₄×C₁₃	D₁₆₉	1	1	yes	characteristic
12	Dic₁₃	—	169	2	no	—
13	C₂×C₁₃	C₂×D₁₆₉	1	1	yes	characteristic
14	C₁₃	Dic₃₃₈	1	1	yes	characteristic
15	Q₈	—	2197	1	no	Sylow
16	C₄	—	2197	2	no	—
17	C₄	D₂₁₉₇	1	1	yes	characteristic
18	C₂	C₂×D₂₁₉₇	1	1	yes	characteristic

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

N	H ≅ G/N	type
4. C₂₁₉₇	Q₈	semidirect

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