Subgroups — #19132811

Order 5504.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₆₈₈	C₂	1	1	yes	maximal, characteristic, complemented
2	D₁₃₇₆	C₂	1	1	yes	maximal, characteristic
3	C₄₃×C₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₃₄₄	—	2	1	no	—
5	D₆₈₈	—	2	1	no	—
6	C₃₂×C₄₃	C₂²	1	1	yes	characteristic
7	Dic₁₇₂	—	4	1	no	—
8	D₃₄₄	—	4	1	no	—
9	C₁₆×C₄₃	D₄	1	1	yes	characteristic
10	D₁₇₂	—	8	1	no	—
11	Dic₈₆	—	8	1	no	—
12	C₈×C₄₃	D₈	1	1	yes	characteristic
13	C₂×D₄₃	—	16	1	no	—
14	C₄×C₄₃	D₁₆	1	1	yes	characteristic
15	Dic₄₃	—	16	1	no	—
16	SD₁₂₈	—	43	1	no	maximal, Sylow
17	C₂×C₄₃	D₃₂	1	1	yes	characteristic
18	D₄₃	—	32	1	no	—
19	Q₆₄	—	43	1	no	—
20	D₃₂	—	43	1	no	—
21	C₆₄	D₄₃	1	1	yes	characteristic, complemented
22	C₄₃	SD₁₂₈	1	1	yes	characteristic, complemented, Sylow
23	Q₃₂	—	86	1	no	—
24	D₁₆	—	86	1	no	—
25	C₃₂	C₂×D₄₃	1	1	yes	characteristic
26	Q₁₆	—	172	1	no	—
27	D₈	—	172	1	no	—
28	C₁₆	D₁₇₂	1	1	yes	characteristic
29	Q₈	—	344	1	no	—
30	D₄	—	344	1	no	—
31	C₈	D₃₄₄	1	1	yes	characteristic
32	C₂²	—	688	1	no	—
33	C₄	—	688	1	no	—
34	C₄	D₆₈₈	1	1	yes	characteristic
35	C₂	—	1376	1	no	—
36	C₂	D₁₃₇₆	1	1	yes	characteristic

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