Subgroups — #39910352

Order 26176.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27189814	C₂	1	2	yes	maximal
2	C₈×#13109888	C₂	1	1	yes	maximal, characteristic
3	#20267000	—	2	2	no	—
4	#20266996	C₂²	1	1	yes	characteristic
5	C₄×#13109888	C₄	1	1	yes	characteristic
6	C₈×D₄₀₉	C₄	1	1	yes	characteristic
7	C₂×#13109888	—	2	1	no	—
8	#15692550	D₄	1	1	yes	characteristic
9	#15692550	Q₈	1	1	yes	characteristic
10	C₄×D₄₀₉	C₂×C₄	1	1	yes	characteristic
11	#15692543	C₈	1	1	yes	characteristic
12	C₈×C₄₀₉	C₈	1	1	yes	characteristic
13	C₂×D₄₀₉	M₁₆	1	1	yes	characteristic
14	#13109888	—	2	2	no	—
15	C₄×C₄₀₉	C₂×C₈	1	1	yes	characteristic
16	Dic₄₀₉	C₄⋊C₄	1	1	yes	characteristic
17	C₂×C₄₀₉	C₄⋊C₈	1	1	yes	characteristic
18	D₄₀₉	—	2	1	no	—
19	C₄₀₉	#364	1	1	yes	characteristic, complemented, Sylow
20	#364	—	409	1	no	maximal, Sylow
21	M₃₂	—	409	2	no	—
22	C₄×C₈	—	409	1	no	—
23	C₂×C₈	—	409	1	no	—
24	C₂×C₈	—	409	1	no	—
25	C₄²	—	409	1	no	—
26	C₁₆	—	818	2	no	—
27	C₂×C₄	—	818	1	no	—
28	C₂×C₄	—	409	1	no	—
29	C₈	—	409	1	no	—
30	C₈	—	409	1	no	—
31	C₈	—	409	1	no	—
32	C₈	#15692552	1	1	yes	characteristic
33	C₂²	—	409	1	no	—
34	C₄	—	818	2	no	—
35	C₄	—	409	1	no	—
36	C₄	C₂×#15692552	1	1	yes	characteristic
37	C₂	—	818	1	no	—
38	C₂	C₄⋊#15692552	1	1	yes	characteristic

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

N	H ≅ G/N	type
19. C₄₀₉	#364	semidirect

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