Subgroups — #35204116

Order 20288.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23778854	C₂	1	2	yes	maximal
2	#23778690	C₂	1	1	yes	maximal, characteristic
3	#19099577	C₄	1	4	yes	complemented
4	C₂×#14579261	C₂²	1	1	yes	characteristic
5	C₄×Dic₃₁₇	C₄	1	1	yes	characteristic
6	C₂×C₈×C₃₁₇	C₄	1	1	yes	characteristic
7	C₂×Dic₃₁₇	—	2	1	no	—
8	#14579261	C₂×C₄	1	2	yes	—
9	C₂×C₄×C₃₁₇	C₂×C₄	1	1	yes	characteristic
10	C₈×C₃₁₇	—	2	1	no	—
11	C₂²×C₃₁₇	M₁₆	1	1	yes	characteristic
12	C₄×C₃₁₇	C₄²	1	1	yes	characteristic
13	C₄×C₃₁₇	M₁₆	1	1	yes	characteristic
14	Dic₃₁₇	—	4	1	no	—
15	C₂×C₃₁₇	—	2	1	no	—
16	C₂×C₃₁₇	#97	1	1	yes	characteristic
17	C₃₁₇	#347	1	1	yes	characteristic, complemented, Sylow
18	#347	—	317	1	no	maximal, Sylow
19	M₃₂	—	317	2	no	—
20	#97	—	317	1	no	—
21	C₂×C₈	—	317	1	no	—
22	C₂×C₈	#11929639	1	1	yes	characteristic
23	C₄²	—	317	1	no	—
24	C₁₆	—	317	4	no	—
25	C₂×C₄	—	634	1	no	—
26	C₂×C₄	C₂×#11929639	1	1	yes	characteristic
27	C₈	—	2	1	no	—
28	C₈	—	317	2	no	—
29	C₂²	#19099584	1	1	yes	characteristic
30	C₄	—	1268	1	no	—
31	C₄	C₄×#11929639	1	1	yes	characteristic
32	C₄	#19099583	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	#23778835	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #19099577	C₄	semidirect
17. C₃₁₇	#347	semidirect

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