Subgroups — #36342165

Order 21568.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24925026	C₂	1	2	yes	maximal
2	#24924957	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582113	—	2	2	no	—
4	C₂×Dic₆₇₄	C₄	1	1	yes	characteristic
5	#19129164	—	2	2	no	—
6	C₄×Dic₃₃₇	C₂²	1	1	yes	characteristic
7	C₂×Q₈×C₃₃₇	C₄	1	1	yes	characteristic
8	#14582113	—	4	2	no	—
9	Dic₆₇₄	—	4	1	no	—
10	C₂×Dic₃₃₇	—	2	1	no	—
11	C₂×Dic₃₃₇	D₄	1	2	yes	—
12	Q₈×C₃₃₇	—	4	1	no	—
13	C₂×C₄×C₃₃₇	—	2	1	no	—
14	C₂×C₄×C₃₃₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₃₃₇	C₂²⋊C₄	1	1	yes	characteristic
16	C₄×C₃₃₇	—	2	1	no	—
17	C₄×C₃₃₇	—	4	1	no	—
18	Dic₃₃₇	—	4	1	no	—
19	Dic₃₃₇	SD₁₆	1	2	yes	—
20	Dic₃₃₇	Q₁₆	1	2	yes	—
21	C₂×C₃₃₇	#100	1	1	yes	characteristic
22	C₂×C₃₃₇	#103	1	2	yes	—
23	C₃₃₇	#333	1	1	yes	characteristic, complemented, Sylow
24	#333	—	337	1	no	maximal, Sylow
25	C₄⋊Q₈	—	337	1	no	—
26	C₄⋊C₈	—	337	2	no	—
27	C₂×Q₈	—	337	1	no	—
28	C₂×Q₈	#13062438	1	1	yes	characteristic
29	C₂×C₈	—	674	2	no	—
30	C₄⋊C₄	—	674	2	no	—
31	C₄²	—	337	1	no	—
32	Q₈	—	4	1	no	—
33	Q₈	—	1348	1	no	—
34	C₂×C₄	—	2	1	no	—
35	C₂×C₄	—	337	2	no	—
36	C₂×C₄	—	674	1	no	—
37	C₂×C₄	C₂×#13062438	1	1	yes	characteristic
38	C₈	—	1348	2	no	—
39	C₂²	C₂²⋊#13062438	1	1	yes	characteristic
40	C₄	—	2	1	no	—
41	C₄	—	4	1	no	—
42	C₄	—	1348	1	no	—
43	C₄	—	337	2	no	—
44	C₄	—	337	2	no	—
45	C₂	#24925019	1	1	yes	characteristic
46	C₂	#24925022	1	2	yes	—

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

N	H ≅ G/N	type
23. C₃₃₇	#333	semidirect

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