Subgroups — C₂²×#14555513 #22578456

Order 8768.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14555513	C₂	1	6	yes	maximal, direct product factor
2	C₂²×#11764040	C₂	1	1	yes	maximal, characteristic
3	#14555513	C₂²	1	4	yes	direct product factor
4	C₂×#11764040	C₄	1	3	yes	—
5	C₂×#11764040	C₂²	1	3	yes	—
6	C₂²×C₄×C₁₃₇	C₄	1	1	yes	characteristic
7	#11764040	C₂×C₄	1	3	yes	—
8	#11764040	C₂³	1	1	yes	characteristic
9	C₂³×C₁₃₇	C₈	1	1	yes	characteristic
10	C₂×C₄×C₁₃₇	C₈	1	3	yes	—
11	C₂×C₄×C₁₃₇	C₂×C₄	1	3	yes	—
12	C₂²×C₁₃₇	C₁₆	1	4	yes	complemented
13	C₂²×C₁₃₇	C₂×C₈	1	3	yes	—
14	C₄×C₁₃₇	C₂×C₈	1	3	yes	—
15	C₄×C₁₃₇	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₁₃₇	C₂×C₁₆	1	6	yes	complemented
17	C₂×C₁₃₇	C₂²×C₈	1	1	yes	characteristic
18	C₁₃₇	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₁₆	—	137	1	no	maximal, Sylow
20	C₂²×C₈	—	137	1	no	—
21	C₂×C₁₆	—	137	6	no	—
22	C₂²×C₄	#10587739	1	1	yes	characteristic
23	C₂×C₈	—	137	3	no	—
24	C₂×C₈	—	137	3	no	—
25	C₁₆	—	137	4	no	—
26	C₂³	#11764047	1	1	yes	characteristic
27	C₂×C₄	#11764047	1	3	yes	—
28	C₂×C₄	C₂×#10587739	1	3	yes	—
29	C₈	—	137	1	no	—
30	C₈	—	137	3	no	—
31	C₂²	#14555513	1	4	yes	direct product factor
32	C₂²	C₂×#11764047	1	3	yes	—
33	C₄	C₂×#11764047	1	3	yes	—
34	C₄	C₂²×#10587739	1	1	yes	characteristic
35	C₂	C₂×#14555513	1	6	yes	direct product factor
36	C₂	C₂²×#11764047	1	1	yes	characteristic

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