Subgroups — #24924881

Order 10784.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃₄₈	C₂	1	1	yes	maximal, characteristic
2	C₄⋊Dic₃₃₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×C₃₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₃₃₇	—	2	1	no	—
5	D₁₃₄₈	—	2	1	no	—
6	D₁₃₄₈	C₄	1	2	yes	complemented
7	C₂×Dic₃₃₇	—	2	1	no	—
8	C₂×C₄×C₃₃₇	C₂²	1	1	yes	characteristic
9	C₈×C₃₃₇	—	2	1	no	—
10	C₂²×C₃₃₇	D₄	1	1	yes	characteristic
11	C₂×D₃₃₇	—	2	2	no	—
12	C₂×D₃₃₇	—	4	1	no	—
13	C₂×D₃₃₇	—	4	1	no	—
14	C₄×C₃₃₇	C₂×C₄	1	1	yes	characteristic
15	C₄×C₃₃₇	D₄	1	1	yes	characteristic
16	Dic₃₃₇	—	4	1	no	—
17	C₂×C₃₃₇	C₂²⋊C₄	1	1	yes	characteristic
18	C₂×C₃₃₇	D₈	1	1	yes	characteristic
19	C₂×C₃₃₇	SD₁₆	1	1	yes	characteristic
20	D₃₃₇	—	4	2	no	—
21	C₃₃₇	#102	1	1	yes	characteristic, complemented, Sylow
22	#102	—	337	1	no	maximal, Sylow
23	C₂×D₄	—	337	1	no	—
24	C₂×C₈	D₃₃₇	1	1	yes	characteristic, complemented
25	C₄⋊C₄	—	337	1	no	—
26	C₂³	—	674	1	no	—
27	D₄	—	337	2	no	—
28	D₄	—	674	1	no	—
29	C₂×C₄	—	674	1	no	—
30	C₂×C₄	C₂×D₃₃₇	1	1	yes	characteristic
31	C₈	—	2	1	no	—
32	C₂²	—	1348	1	no	—
33	C₂²	—	1348	1	no	—
34	C₂²	—	674	2	no	—
35	C₂²	D₁₃₄₈	1	1	yes	characteristic
36	C₄	—	1348	1	no	—
37	C₄	C₄×D₃₃₇	1	1	yes	characteristic
38	C₄	C₂²⋊D₃₃₇	1	1	yes	characteristic
39	C₂	—	1348	2	no	—
40	C₂	#19129162	1	1	yes	characteristic
41	C₂	D₂₆₉₆	1	1	yes	characteristic
42	C₂	#19129174	1	1	yes	characteristic

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