Subgroups — #22577236

Order 8768.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₆×D₁₃₇	C₂	1	1	yes	maximal, characteristic
2	#17983994	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃₂×C₁₃₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×D₁₃₇	C₄	1	1	yes	characteristic
5	#14555485	C₄	1	1	yes	characteristic
6	C₁₆×C₁₃₇	C₂²	1	1	yes	characteristic
7	C₄×D₁₃₇	C₈	1	1	yes	characteristic
8	#11764040	C₈	1	1	yes	characteristic
9	C₈×C₁₃₇	C₂×C₄	1	1	yes	characteristic
10	C₂×D₁₃₇	C₁₆	1	1	yes	characteristic
11	C₄×C₁₃₇	C₂×C₈	1	1	yes	characteristic
12	Dic₁₃₇	C₁₆	1	1	yes	characteristic
13	C₂×C₁₃₇	C₂×C₁₆	1	1	yes	characteristic
14	D₁₃₇	—	2	1	no	—
15	C₁₃₇	M₆₄	1	1	yes	characteristic, complemented, Sylow
16	M₆₄	—	137	1	no	maximal, Sylow
17	C₂×C₁₆	—	137	1	no	—
18	C₃₂	—	137	1	no	—
19	C₃₂	D₁₃₇	1	1	yes	characteristic, complemented
20	C₂×C₈	—	137	1	no	—
21	C₁₆	—	137	1	no	—
22	C₁₆	C₂×D₁₃₇	1	1	yes	characteristic
23	C₂×C₄	—	137	1	no	—
24	C₈	—	137	1	no	—
25	C₈	C₄×D₁₃₇	1	1	yes	characteristic
26	C₂²	—	137	1	no	—
27	C₄	—	137	1	no	—
28	C₄	C₈×D₁₃₇	1	1	yes	characteristic
29	C₂	—	274	1	no	—
30	C₂	C₁₆×D₁₃₇	1	1	yes	characteristic

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