Subgroups — #20298424

Order 7232.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16813556	C₂	1	2	yes	maximal
2	C₂×C₁₆×C₁₁₃	C₂	1	1	yes	maximal, characteristic
3	C₄⋊Dic₁₁₃	—	2	2	no	—
4	C₂×C₈×C₁₁₃	C₂²	1	1	yes	characteristic
5	C₁₆×C₁₁₃	C₄	1	2	yes	complemented
6	C₂×C₄×C₁₁₃	D₄	1	1	yes	characteristic
7	C₂×Dic₁₁₃	—	4	2	no	—
8	C₈×C₁₁₃	C₂×C₄	1	1	yes	characteristic
9	C₈×C₁₁₃	Q₈	1	1	yes	characteristic
10	C₂²×C₁₁₃	D₈	1	1	yes	characteristic
11	C₄×C₁₁₃	C₄⋊C₄	1	1	yes	characteristic
12	C₄×C₁₁₃	Q₁₆	1	1	yes	characteristic
13	Dic₁₁₃	—	8	2	no	—
14	C₂×C₁₁₃	#107	1	1	yes	characteristic
15	C₂×C₁₁₃	D₁₆	1	1	yes	characteristic
16	C₂×C₁₁₃	Q₃₂	1	1	yes	characteristic
17	C₁₁₃	#366	1	1	yes	characteristic, complemented, Sylow
18	#366	—	113	1	no	maximal, Sylow
19	C₂×C₁₆	D₁₁₃	1	1	yes	characteristic
20	#107	—	113	2	no	—
21	C₂×C₈	C₂×D₁₁₃	1	1	yes	characteristic
22	C₄⋊C₄	—	226	2	no	—
23	C₁₆	Dic₁₁₃	1	2	yes	complemented
24	C₂×C₄	—	452	2	no	—
25	C₂×C₄	D₄₅₂	1	1	yes	characteristic
26	C₈	Dic₂₂₆	1	1	yes	characteristic
27	C₈	C₂×Dic₁₁₃	1	1	yes	characteristic
28	C₂²	D₉₀₄	1	1	yes	characteristic
29	C₄	—	904	2	no	—
30	C₄	C₄⋊Dic₁₁₃	1	1	yes	characteristic
31	C₄	Dic₄₅₂	1	1	yes	characteristic
32	C₂	#16813556	1	1	yes	characteristic
33	C₂	D₁₈₀₈	1	1	yes	characteristic
34	C₂	Dic₉₀₄	1	1	yes	characteristic

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