Subgroups — #20299486

Order 7232.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14268650	C₂	1	2	yes	maximal
2	C₄×#11744751	C₂	1	1	yes	maximal, characteristic
3	#14268650	C₄	1	4	yes	complemented
4	C₂×#11744751	C₄	1	1	yes	characteristic
5	C₂×#11744751	C₂²	1	1	yes	characteristic
6	C₄²×C₁₁₃	C₄	1	1	yes	characteristic
7	C₂×C₄×C₁₁₃	C₈	1	2	yes	—
8	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
9	#11744751	C₈	1	2	yes	—
10	#11744751	C₂×C₄	1	2	yes	—
11	C₂²×C₁₁₃	C₂×C₈	1	1	yes	characteristic
12	C₄×C₁₁₃	—	2	2	no	—
13	C₄×C₁₁₃	C₄²	1	1	yes	characteristic
14	C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
15	C₂×C₁₁₃	C₄×C₈	1	1	yes	characteristic
16	C₂×C₁₁₃	M₃₂	1	2	yes	—
17	C₁₁₃	#346	1	1	yes	characteristic, complemented, Sylow
18	#346	—	113	1	no	maximal, Sylow
19	C₂×C₁₆	—	113	2	no	—
20	C₄×C₈	—	113	1	no	—
21	C₂×C₈	—	113	1	no	—
22	C₂×C₈	—	113	1	no	—
23	C₄²	#90673	1	1	yes	characteristic
24	C₁₆	—	113	4	no	—
25	C₂×C₄	#11744753	1	2	yes	—
26	C₂×C₄	C₂×#90673	1	1	yes	characteristic
27	C₈	—	113	2	no	—
28	C₈	—	113	2	no	—
29	C₂²	C₂×#11744753	1	1	yes	characteristic
30	C₄	—	2	2	no	—
31	C₄	C₄×#90673	1	1	yes	characteristic
32	C₄	#14268655	1	1	yes	characteristic
33	C₂	C₄×#11744753	1	1	yes	characteristic
34	C₂	#16813696	1	2	yes	—

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

N	H ≅ G/N	type
3. #14268650	C₄	semidirect
17. C₁₁₃	#346	semidirect