Subgroups — #24924893

Order 10784.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Dic₃₃₇	C₂	1	2	yes	maximal
2	C₂×C₈×C₃₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₃₃₇	—	2	2	no	—
4	C₂×C₄×C₃₃₇	C₂²	1	1	yes	characteristic
5	C₈×C₃₃₇	C₄	1	2	yes	complemented
6	C₂²×C₃₃₇	D₄	1	1	yes	characteristic
7	C₄×C₃₃₇	C₂×C₄	1	1	yes	characteristic
8	C₄×C₃₃₇	Q₈	1	1	yes	characteristic
9	Dic₃₃₇	—	4	2	no	—
10	C₂×C₃₃₇	C₄⋊C₄	1	1	yes	characteristic
11	C₂×C₃₃₇	D₈	1	1	yes	characteristic
12	C₂×C₃₃₇	Q₁₆	1	1	yes	characteristic
13	C₃₃₇	#107	1	1	yes	characteristic, complemented, Sylow
14	#107	—	337	1	no	maximal, Sylow
15	C₂×C₈	D₃₃₇	1	1	yes	characteristic
16	C₄⋊C₄	—	337	2	no	—
17	C₂×C₄	—	674	2	no	—
18	C₂×C₄	C₂×D₃₃₇	1	1	yes	characteristic
19	C₈	Dic₃₃₇	1	2	yes	complemented
20	C₂²	D₁₃₄₈	1	1	yes	characteristic
21	C₄	—	1348	2	no	—
22	C₄	C₂×Dic₃₃₇	1	1	yes	characteristic
23	C₄	Dic₆₇₄	1	1	yes	characteristic
24	C₂	C₄⋊Dic₃₃₇	1	1	yes	characteristic
25	C₂	D₂₆₉₆	1	1	yes	characteristic
26	C₂	Dic₁₃₄₈	1	1	yes	characteristic

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