Subgroups — #34095008

Order 20032.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23756552	C₂	1	2	yes	maximal, complemented
2	#23756486	C₂	1	1	yes	maximal, characteristic
3	C₂×#14578816	—	2	2	no	—
4	C₂×D₁₂₅₂	C₄	1	1	yes	characteristic
5	#19097538	—	2	2	no	—
6	C₄×Dic₃₁₃	C₂²	1	1	yes	characteristic
7	C₂×Q₈×C₃₁₃	C₄	1	1	yes	characteristic
8	#14578816	—	2	4	no	—
9	C₂²×D₃₁₃	—	2	1	no	—
10	D₁₂₅₂	—	4	1	no	—
11	C₂×Dic₃₁₃	D₄	1	2	yes	—
12	Q₈×C₃₁₃	—	4	1	no	—
13	C₂×C₄×C₃₁₃	—	2	1	no	—
14	C₂×C₄×C₃₁₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₃₁₃	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×D₃₁₃	—	4	1	no	—
17	C₂×D₃₁₃	—	4	2	no	—
18	C₄×C₃₁₃	—	2	1	no	—
19	C₄×C₃₁₃	—	4	1	no	—
20	Dic₃₁₃	—	2	2	no	—
21	C₂×C₃₁₃	#100	1	1	yes	characteristic
22	C₂×C₃₁₃	#104	1	2	yes	—
23	D₃₁₃	—	8	1	no	—
24	C₃₁₃	#329	1	1	yes	characteristic, complemented, Sylow
25	#329	—	313	1	no	maximal, Sylow
26	#124	—	313	1	no	—
27	#97	—	313	2	no	—
28	C₂×Q₈	#11929411	1	1	yes	characteristic
29	C₂×D₄	—	313	1	no	—
30	C₂×C₈	—	626	2	no	—
31	C₂²⋊C₄	—	626	2	no	—
32	C₄²	—	313	1	no	—
33	C₂³	—	626	1	no	—
34	Q₈	—	4	1	no	—
35	D₄	—	1252	1	no	—
36	C₂×C₄	—	2	1	no	—
37	C₂×C₄	—	313	2	no	—
38	C₂×C₄	C₂×#11929411	1	1	yes	characteristic
39	C₈	—	626	4	no	—
40	C₂²	—	1252	1	no	—
41	C₂²	—	1252	2	no	—
42	C₂²	C₂²⋊#11929411	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	4	1	no	—
45	C₄	—	626	2	no	—
46	C₂	—	2504	1	no	—
47	C₂	#23756557	1	1	yes	characteristic
48	C₂	#23756562	1	2	yes	—

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

N	H ≅ G/N	type
1. #23756552	C₂	semidirect
24. C₃₁₃	#329	semidirect

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