Subgroups — #20299720

Order 7232.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813719	C₂	1	3	yes	maximal, complemented
2	#16813717	C₂	1	3	yes	maximal, complemented
3	#16813710	C₂	1	1	yes	maximal, characteristic
4	#14268659	C₂²	1	1	yes	characteristic
5	#14268659	C₂²	1	3	yes	—
6	#14268657	C₄	1	3	yes	—
7	#14268655	C₂²	1	3	yes	—
8	#14268648	C₄	1	1	yes	characteristic
9	Q₈×C₁₁₃	C₈	1	1	yes	characteristic
10	D₄₅₂	C₈	1	3	yes	—
11	C₄×D₁₁₃	C₂×C₄	1	3	yes	—
12	#11744753	C₂×C₄	1	3	yes	—
13	#11744753	C₂³	1	1	yes	characteristic
14	C₂×D₁₁₃	C₂×C₈	1	3	yes	—
15	C₄×C₁₁₃	C₂×C₈	1	3	yes	—
16	Dic₁₁₃	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₁₁₃	C₂²×C₈	1	1	yes	characteristic
18	D₁₁₃	—	2	3	no	—
19	C₁₁₃	#504	1	1	yes	characteristic, complemented, Sylow
20	#504	—	113	1	no	maximal, Sylow
21	#131	—	113	1	no	—
22	M₃₂	—	113	3	no	—
23	C₂×C₁₆	—	113	3	no	—
24	#41	—	113	1	no	—
25	M₁₆	—	113	3	no	—
26	C₂×C₈	—	113	3	no	—
27	C₁₆	—	113	1	no	—
28	C₁₆	—	113	3	no	—
29	Q₈	#11744762	1	1	yes	characteristic
30	D₄	—	113	3	no	—
31	C₂×C₄	—	113	3	no	—
32	C₈	—	113	1	no	—
33	C₈	—	113	3	no	—
34	C₂²	—	113	3	no	—
35	C₄	—	113	1	no	—
36	C₄	C₂×#11744762	1	3	yes	—
37	C₂	—	226	3	no	—
38	C₂	C₂²×#11744762	1	1	yes	characteristic

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