Subgroups — #24923095

Order 10688.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19128766	C₂	1	2	yes	maximal
2	C₂×C₁₆×C₁₆₇	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₁₆₇	—	2	2	no	—
4	C₂×C₈×C₁₆₇	C₂²	1	1	yes	characteristic
5	C₁₆×C₁₆₇	C₄	1	2	yes	complemented
6	C₂×Dic₁₆₇	—	4	2	no	—
7	C₂×C₄×C₁₆₇	D₄	1	1	yes	characteristic
8	C₈×C₁₆₇	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₆₇	Q₈	1	1	yes	characteristic
10	C₂²×C₁₆₇	D₈	1	1	yes	characteristic
11	C₄×C₁₆₇	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₁₆₇	Q₁₆	1	1	yes	characteristic
13	Dic₁₆₇	—	8	2	no	—
14	C₂×C₁₆₇	#107	1	1	yes	characteristic
15	C₂×C₁₆₇	D₁₆	1	1	yes	characteristic
16	C₂×C₁₆₇	Q₃₂	1	1	yes	characteristic
17	C₁₆₇	#366	1	1	yes	characteristic, complemented, Sylow
18	#366	—	167	1	no	maximal, Sylow
19	C₂×C₁₆	D₁₆₇	1	1	yes	characteristic
20	#107	—	167	2	no	—
21	C₂×C₈	C₂×D₁₆₇	1	1	yes	characteristic
22	C₄⋊C₄	—	334	2	no	—
23	C₁₆	Dic₁₆₇	1	2	yes	complemented
24	C₂×C₄	—	668	2	no	—
25	C₂×C₄	D₆₆₈	1	1	yes	characteristic
26	C₈	C₂×Dic₁₆₇	1	1	yes	characteristic
27	C₈	Dic₃₃₄	1	1	yes	characteristic
28	C₂²	D₁₃₃₆	1	1	yes	characteristic
29	C₄	—	1336	2	no	—
30	C₄	C₄⋊Dic₁₆₇	1	1	yes	characteristic
31	C₄	Dic₆₆₈	1	1	yes	characteristic
32	C₂	#19128766	1	1	yes	characteristic
33	C₂	D₂₆₇₂	1	1	yes	characteristic
34	C₂	Dic₁₃₃₆	1	1	yes	characteristic

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