Subgroups — #36342404

Order 21568.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24925055	C₂	1	2	yes	maximal, complemented
2	C₂×#19129195	C₂	1	1	yes	maximal, characteristic
3	#19129197	—	2	2	no	—
4	#19129195	—	2	2	no	—
5	C₂×#14582113	C₄	1	1	yes	characteristic
6	C₂×#14582113	C₂²	1	1	yes	characteristic
7	C₂×C₄×D₃₃₇	C₄	1	1	yes	characteristic
8	#14582113	—	2	1	no	—
9	#14582113	D₄	1	2	yes	—
10	C₂²×D₃₃₇	C₈	1	1	yes	characteristic
11	C₂×Dic₃₃₇	C₂×C₄	1	1	yes	characteristic
12	C₄×D₃₃₇	—	2	1	no	—
13	C₄×D₃₃₇	—	2	1	no	—
14	C₂×C₄×C₃₃₇	C₈	1	1	yes	characteristic
15	C₂²×C₃₃₇	C₂×C₈	1	1	yes	characteristic
16	C₂×D₃₃₇	—	2	1	no	—
17	C₂×D₃₃₇	—	4	1	no	—
18	C₄×C₃₃₇	—	2	1	no	—
19	Dic₃₃₇	C₂²⋊C₄	1	1	yes	characteristic
20	Dic₃₃₇	M₁₆	1	1	yes	characteristic
21	C₂×C₃₃₇	—	2	1	no	—
22	C₂×C₃₃₇	C₂²⋊C₈	1	1	yes	characteristic
23	D₃₃₇	—	4	1	no	—
24	C₃₃₇	#349	1	1	yes	characteristic, complemented, Sylow
25	#349	—	337	1	no	maximal, Sylow
26	C₂×M₁₆	—	337	1	no	—
27	M₃₂	—	337	2	no	—
28	C₂²×C₄	—	337	1	no	—
29	M₁₆	—	674	2	no	—
30	C₂×C₈	—	337	1	no	—
31	C₂×C₈	—	337	1	no	—
32	C₁₆	—	674	2	no	—
33	C₂³	—	337	1	no	—
34	C₂×C₄	—	337	1	no	—
35	C₂×C₄	—	674	1	no	—
36	C₂×C₄	—	674	1	no	—
37	C₂×C₄	#14582115	1	1	yes	characteristic
38	C₈	—	337	2	no	—
39	C₈	—	674	1	no	—
40	C₂²	—	1348	1	no	—
41	C₂²	—	674	1	no	—
42	C₂²	C₂×#14582115	1	1	yes	characteristic
43	C₄	—	2	1	no	—
44	C₄	—	337	1	no	—
45	C₄	—	337	1	no	—
46	C₂	—	2	1	no	—
47	C₂	—	1348	1	no	—
48	C₂	C₂²⋊#14582115	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #24925055	C₂	semidirect
24. C₃₃₇	#349	semidirect

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