Subgroups — #20299521

Order 7232.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813696	C₂	1	2	yes	maximal
2	C₄×#11744751	C₂	1	1	yes	maximal, characteristic
3	#14268650	—	2	2	no	—
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	—	2	1	no	—
8	C₂×C₄×C₁₁₃	C₂×C₄	1	1	yes	characteristic
9	#11744751	C₈	1	2	yes	—
10	#11744751	D₄	1	1	yes	characteristic
11	#11744751	Q₈	1	1	yes	characteristic
12	C₂²×C₁₁₃	M₁₆	1	1	yes	characteristic
13	C₄×C₁₁₃	—	2	2	no	—
14	C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₁₁₃	C₂×C₈	1	1	yes	characteristic
16	C₂×C₁₁₃	—	2	1	no	—
17	C₂×C₁₁₃	C₄⋊C₈	1	1	yes	characteristic
18	C₁₁₃	#364	1	1	yes	characteristic, complemented, Sylow
19	#364	—	113	1	no	maximal, Sylow
20	M₃₂	—	113	2	no	—
21	C₄×C₈	—	113	1	no	—
22	C₂×C₈	—	113	1	no	—
23	C₂×C₈	—	113	1	no	—
24	C₄²	#90673	1	1	yes	characteristic
25	C₁₆	—	226	2	no	—
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	C₂×#90673	1	1	yes	characteristic
28	C₈	—	113	1	no	—
29	C₈	—	113	1	no	—
30	C₈	—	113	2	no	—
31	C₂²	#14268656	1	1	yes	characteristic
32	C₄	—	2	2	no	—
33	C₄	C₄⋊#90673	1	1	yes	characteristic
34	C₄	#14268655	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#16813689	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₁₁₃	#364	semidirect