Subgroups — #35229672

Order 20896.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₂₆₁₂	C₂	1	1	yes	maximal, characteristic, complemented
2	D₅₂₂₄	C₂	1	1	yes	maximal, characteristic
3	C₁₆×C₆₅₃	C₂	1	1	yes	maximal, characteristic, complemented
4	Dic₁₃₀₆	—	2	1	no	—
5	D₂₆₁₂	—	2	1	no	—
6	C₈×C₆₅₃	C₂²	1	1	yes	characteristic
7	C₂×D₆₅₃	—	4	1	no	—
8	C₄×C₆₅₃	D₄	1	1	yes	characteristic
9	Dic₆₅₃	—	4	1	no	—
10	C₂×C₆₅₃	D₈	1	1	yes	characteristic
11	D₆₅₃	—	8	1	no	—
12	C₆₅₃	SD₃₂	1	1	yes	characteristic, complemented, Sylow
13	SD₃₂	—	653	1	no	maximal, Sylow
14	Q₁₆	—	653	1	no	—
15	D₈	—	653	1	no	—
16	C₁₆	D₆₅₃	1	1	yes	characteristic, complemented
17	Q₈	—	1306	1	no	—
18	D₄	—	1306	1	no	—
19	C₈	C₂×D₆₅₃	1	1	yes	characteristic
20	C₂²	—	2612	1	no	—
21	C₄	—	2612	1	no	—
22	C₄	D₂₆₁₂	1	1	yes	characteristic
23	C₂	—	5224	1	no	—
24	C₂	D₅₂₂₄	1	1	yes	characteristic

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

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.