Subgroups — #19104735

Order 5216.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₃₂₆	C₂	1	2	yes	maximal
2	C₄⋊Dic₁₆₃	C₂	1	4	yes	maximal
3	C₄²×C₁₆₃	C₂	1	1	yes	maximal, characteristic
4	Dic₃₂₆	—	2	4	no	—
5	C₂×Dic₁₆₃	C₂²	1	4	yes	—
6	C₂×C₄×C₁₆₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₁₆₃	C₂²	1	2	yes	—
8	C₂²×C₁₆₃	C₂³	1	1	yes	characteristic
9	C₄×C₁₆₃	D₄	1	2	yes	—
10	C₄×C₁₆₃	Q₈	1	4	yes	complemented
11	Dic₁₆₃	—	2	4	no	—
12	C₂×C₁₆₃	C₂×D₄	1	1	yes	characteristic
13	C₂×C₁₆₃	C₂×Q₈	1	2	yes	—
14	C₁₆₃	C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
15	C₄⋊Q₈	—	163	1	no	maximal, Sylow
16	C₂×Q₈	—	163	2	no	—
17	C₄⋊C₄	—	163	4	no	—
18	C₄²	D₁₆₃	1	1	yes	characteristic
19	Q₈	—	326	4	no	—
20	C₂×C₄	—	163	4	no	—
21	C₂×C₄	C₂×D₁₆₃	1	1	yes	characteristic
22	C₂×C₄	C₂×D₁₆₃	1	2	yes	—
23	C₂²	C₂²×D₁₆₃	1	1	yes	characteristic
24	C₄	—	326	4	no	—
25	C₄	D₆₅₂	1	2	yes	—
26	C₄	Dic₃₂₆	1	4	yes	complemented
27	C₂	C₂×D₆₅₂	1	1	yes	characteristic
28	C₂	C₂×Dic₃₂₆	1	2	yes	—

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