Subgroups — #39905743

Order 25888.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₂₃₆	C₂	1	1	yes	maximal, characteristic, complemented
2	#27188218	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×C₈₀₉	C₂	1	1	yes	maximal, characteristic
4	Dic₁₆₁₈	—	2	1	no	—
5	D₄×C₈₀₉	—	2	1	no	—
6	C₈×C₈₀₉	C₂²	1	1	yes	characteristic
7	C₂²×C₈₀₉	—	4	1	no	—
8	C₄×C₈₀₉	D₄	1	1	yes	characteristic
9	Dic₈₀₉	—	4	1	no	—
10	C₂×C₈₀₉	—	8	1	no	—
11	C₂×C₈₀₉	D₈	1	1	yes	characteristic
12	C₈₀₉	SD₃₂	1	1	yes	characteristic, complemented, Sylow
13	SD₃₂	—	809	1	no	maximal, Sylow
14	Q₁₆	—	809	1	no	—
15	D₈	D₈₀₉	1	1	yes	characteristic
16	C₁₆	—	809	1	no	—
17	Q₈	—	1618	1	no	—
18	D₄	—	2	1	no	—
19	C₈	C₂×D₈₀₉	1	1	yes	characteristic
20	C₂²	—	4	1	no	—
21	C₄	—	3236	1	no	—
22	C₄	C₂²⋊D₈₀₉	1	1	yes	characteristic
23	C₂	—	8	1	no	—
24	C₂	#27188228	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.