Subgroups — #34089757

Order 19744.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19096928	C₂	1	2	yes	maximal
2	C₄×Dic₆₁₇	C₂	1	1	yes	maximal, characteristic
3	#19096928	C₄	1	4	yes	complemented
4	C₂×Dic₆₁₇	C₄	1	1	yes	characteristic
5	C₂×Dic₆₁₇	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₆₁₇	C₄	1	1	yes	characteristic
7	C₂²×C₆₁₇	C₂×C₄	1	1	yes	characteristic
8	C₄×C₆₁₇	—	2	1	no	—
9	Dic₆₁₇	—	2	1	no	—
10	Dic₆₁₇	C₂×C₄	1	2	yes	—
11	C₂×C₆₁₇	C₄²	1	1	yes	characteristic
12	C₂×C₆₁₇	M₁₆	1	1	yes	characteristic
13	C₂×C₆₁₇	M₁₆	1	1	yes	characteristic
14	C₆₁₇	#97	1	1	yes	characteristic, complemented, Sylow
15	#97	—	617	1	no	maximal, Sylow
16	C₂×C₈	—	617	2	no	—
17	C₄²	—	617	1	no	—
18	C₂×C₄	—	617	1	no	—
19	C₂×C₄	—	617	1	no	—
20	C₂×C₄	#14578674	1	1	yes	characteristic
21	C₈	—	617	4	no	—
22	C₂²	C₂×#14578674	1	1	yes	characteristic
23	C₄	—	2	1	no	—
24	C₄	—	617	2	no	—
25	C₄	—	1234	1	no	—
26	C₂	C₄×#14578674	1	1	yes	characteristic
27	C₂	#23754609	1	1	yes	characteristic
28	C₂	#23754610	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #19096928	C₄	semidirect
14. C₆₁₇	#97	semidirect

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