Subgroups — #20298437

Order 7232.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₉₀₄	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₈₀₈	C₂	1	1	yes	maximal, characteristic
3	C₃₂×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₄₅₂	—	2	1	no	—
5	D₉₀₄	—	2	1	no	—
6	C₁₆×C₁₁₃	C₂²	1	1	yes	characteristic
7	D₄₅₂	—	4	1	no	—
8	Dic₂₂₆	—	4	1	no	—
9	C₈×C₁₁₃	D₄	1	1	yes	characteristic
10	C₂×D₁₁₃	—	8	1	no	—
11	C₄×C₁₁₃	D₈	1	1	yes	characteristic
12	Dic₁₁₃	—	8	1	no	—
13	C₂×C₁₁₃	D₁₆	1	1	yes	characteristic
14	D₁₁₃	—	16	1	no	—
15	C₁₁₃	SD₆₄	1	1	yes	characteristic, complemented, Sylow
16	SD₆₄	—	113	1	no	maximal, Sylow
17	Q₃₂	—	113	1	no	—
18	D₁₆	—	113	1	no	—
19	C₃₂	D₁₁₃	1	1	yes	characteristic, complemented
20	Q₁₆	—	226	1	no	—
21	D₈	—	226	1	no	—
22	C₁₆	C₂×D₁₁₃	1	1	yes	characteristic
23	Q₈	—	452	1	no	—
24	D₄	—	452	1	no	—
25	C₈	D₄₅₂	1	1	yes	characteristic
26	C₂²	—	904	1	no	—
27	C₄	—	904	1	no	—
28	C₄	D₉₀₄	1	1	yes	characteristic
29	C₂	—	1808	1	no	—
30	C₂	D₁₈₀₈	1	1	yes	characteristic

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