Subgroups — #22577124

Order 8768.

66 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#11764040	C₂	1	2	yes	maximal
2	C₄×C₈×C₁₃₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#11764040	C₄	1	4	yes	—
4	C₂×C₈×C₁₃₇	C₄	1	2	yes	—
5	C₄²×C₁₃₇	C₂²	1	1	yes	characteristic
6	#11764040	—	2	4	no	—
7	C₂×C₄×C₁₃₇	C₂×C₄	1	2	yes	—
8	C₂×C₄×C₁₃₇	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₃₇	C₈	1	4	yes	complemented
10	C₂²×C₁₃₇	C₄²	1	1	yes	characteristic
11	C₄×C₁₃₇	C₂×C₈	1	2	yes	—
12	C₄×C₁₃₇	M₁₆	1	4	yes	—
13	C₂×C₁₃₇	C₄×C₈	1	1	yes	characteristic
14	C₂×C₁₃₇	#97	1	2	yes	—
15	C₁₃₇	#322	1	1	yes	characteristic, complemented, Sylow
16	#322	—	137	1	no	maximal, Sylow
17	C₄×C₈	—	137	2	no	—
18	C₄×C₈	D₁₃₇	1	1	yes	characteristic
19	C₂×C₈	—	137	4	no	—
20	C₂×C₈	Dic₁₃₇	1	2	yes	—
21	C₄²	C₂×D₁₃₇	1	1	yes	characteristic
22	C₂×C₄	C₄×D₁₃₇	1	2	yes	—
23	C₂×C₄	C₂×Dic₁₃₇	1	1	yes	characteristic
24	C₈	—	274	4	no	—
25	C₈	#11764040	1	4	yes	complemented
26	C₂²	C₄×Dic₁₃₇	1	1	yes	characteristic
27	C₄	C₂×#11764040	1	2	yes	—
28	C₄	#14555493	1	4	yes	—
29	C₂	C₄×#11764040	1	1	yes	characteristic
30	C₂	#17983998	1	2	yes	—

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