Subgroups — #24924882

Order 10784.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₆₇₄	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582106	C₂	1	1	yes	maximal, characteristic
3	C₄⋊C₄×C₃₃₇	C₂	1	1	yes	maximal, characteristic
4	Dic₆₇₄	—	2	1	no	—
5	Dic₆₇₄	C₄	1	2	yes	complemented
6	C₂×Dic₃₃₇	—	2	1	no	—
7	#14582106	—	2	1	no	—
8	C₂×C₄×C₃₃₇	—	2	1	no	—
9	C₂×C₄×C₃₃₇	C₂²	1	1	yes	characteristic
10	C₂²×C₃₃₇	D₄	1	1	yes	characteristic
11	C₄×C₃₃₇	—	4	1	no	—
12	C₄×C₃₃₇	C₂×C₄	1	1	yes	characteristic
13	C₄×C₃₃₇	D₄	1	1	yes	characteristic
14	Dic₃₃₇	—	2	2	no	—
15	C₂×C₃₃₇	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×C₃₃₇	SD₁₆	1	1	yes	characteristic
17	C₂×C₃₃₇	Q₁₆	1	1	yes	characteristic
18	C₃₃₇	#103	1	1	yes	characteristic, complemented, Sylow
19	#103	—	337	1	no	maximal, Sylow
20	C₂×Q₈	—	337	1	no	—
21	C₂×C₈	—	337	1	no	—
22	C₄⋊C₄	D₃₃₇	1	1	yes	characteristic
23	Q₈	—	337	2	no	—
24	Q₈	—	674	1	no	—
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	—	674	1	no	—
27	C₂×C₄	C₂×D₃₃₇	1	1	yes	characteristic
28	C₈	—	674	1	no	—
29	C₂²	C₂²⋊D₃₃₇	1	1	yes	characteristic
30	C₄	—	4	1	no	—
31	C₄	—	674	2	no	—
32	C₄	C₄×D₃₃₇	1	1	yes	characteristic
33	C₄	D₁₃₄₈	1	1	yes	characteristic
34	C₂	#19129162	1	1	yes	characteristic
35	C₂	#19129173	1	1	yes	characteristic
36	C₂	#19129175	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. Dic₆₇₄	C₄	semidirect
18. C₃₃₇	#103	semidirect