Subgroups — #34089613

Order 19744.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19096921	C₂	1	2	yes	maximal
2	C₄²×C₆₁₇	C₂	1	1	yes	maximal, characteristic
3	#19096921	C₄	1	4	yes	complemented
4	C₂×C₄×C₆₁₇	C₄	1	2	yes	—
5	C₂×C₄×C₆₁₇	C₂²	1	1	yes	characteristic
6	C₂²×C₆₁₇	C₂×C₄	1	1	yes	characteristic
7	C₄×C₆₁₇	—	2	2	no	—
8	C₄×C₆₁₇	C₂×C₄	1	2	yes	—
9	C₂×C₆₁₇	C₄²	1	1	yes	characteristic
10	C₂×C₆₁₇	M₁₆	1	2	yes	—
11	C₆₁₇	#97	1	1	yes	characteristic, complemented, Sylow
12	#97	—	617	1	no	maximal, Sylow
13	C₂×C₈	—	617	2	no	—
14	C₄²	D₆₁₇	1	1	yes	characteristic
15	C₂×C₄	Dic₆₁₇	1	2	yes	—
16	C₂×C₄	C₂×D₆₁₇	1	1	yes	characteristic
17	C₈	—	617	4	no	—
18	C₂²	C₂×Dic₆₁₇	1	1	yes	characteristic
19	C₄	—	2	2	no	—
20	C₄	C₄×D₆₁₇	1	2	yes	—
21	C₂	C₄×Dic₆₁₇	1	1	yes	characteristic
22	C₂	#23754584	1	2	yes	—

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

N	H ≅ G/N	type
3. #19096921	C₄	semidirect
11. C₆₁₇	#97	semidirect

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