Subgroups — #20299692

Order 7232.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268659	C₂	1	2	yes	maximal
2	C₄×#11744753	C₂	1	1	yes	maximal, characteristic
3	#14268659	C₄	1	4	yes	complemented
4	C₂×#11744753	C₄	1	1	yes	characteristic
5	C₂×#11744753	C₂²	1	1	yes	characteristic
6	C₄×Dic₁₁₃	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₁₃	C₈	1	1	yes	characteristic
8	C₂×Dic₁₁₃	C₈	1	1	yes	characteristic
9	C₂×Dic₁₁₃	C₂×C₄	1	1	yes	characteristic
10	#11744753	C₈	1	2	yes	—
11	#11744753	C₂×C₄	1	2	yes	—
12	C₂²×C₁₁₃	C₂×C₈	1	1	yes	characteristic
13	C₄×C₁₁₃	—	2	1	no	—
14	Dic₁₁₃	—	2	1	no	—
15	Dic₁₁₃	C₄²	1	1	yes	characteristic
16	Dic₁₁₃	C₂×C₈	1	1	yes	characteristic
17	C₂×C₁₁₃	C₄×C₈	1	1	yes	characteristic
18	C₂×C₁₁₃	M₃₂	1	1	yes	characteristic
19	C₂×C₁₁₃	M₃₂	1	1	yes	characteristic
20	C₁₁₃	#346	1	1	yes	characteristic, complemented, Sylow
21	#346	—	113	1	no	maximal, Sylow
22	C₂×C₁₆	—	113	2	no	—
23	C₄×C₈	—	113	1	no	—
24	C₂×C₈	—	113	1	no	—
25	C₂×C₈	—	113	1	no	—
26	C₄²	—	113	1	no	—
27	C₁₆	—	113	4	no	—
28	C₂×C₄	—	113	1	no	—
29	C₂×C₄	—	113	1	no	—
30	C₂×C₄	#11744762	1	1	yes	characteristic
31	C₈	—	113	2	no	—
32	C₈	—	113	2	no	—
33	C₂²	C₂×#11744762	1	1	yes	characteristic
34	C₄	—	2	1	no	—
35	C₄	—	113	1	no	—
36	C₄	—	113	1	no	—
37	C₄	—	226	1	no	—
38	C₂	C₄×#11744762	1	1	yes	characteristic
39	C₂	#16813718	1	1	yes	characteristic
40	C₂	#16813719	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #14268659	C₄	semidirect
20. C₁₁₃	#346	semidirect