Subgroups — #41001503

Order 26848.

24 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Dic₃₃₅₆	C₂	1	1	yes	maximal, characteristic
2	C₈₃₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×C₈₃₉	C₂	1	1	yes	maximal, characteristic
4	Dic₁₆₇₈	—	2	1	no	—
5	Q₈×C₈₃₉	—	2	1	no	—
6	C₈×C₈₃₉	C₂²	1	1	yes	characteristic
7	C₄×C₈₃₉	—	4	1	no	—
8	C₄×C₈₃₉	D₄	1	1	yes	characteristic
9	Dic₈₃₉	—	4	1	no	—
10	C₂×C₈₃₉	D₈	1	1	yes	characteristic
11	C₈₃₉	Q₃₂	1	1	yes	characteristic, complemented, Sylow
12	Q₃₂	—	839	1	no	maximal, Sylow
13	Q₁₆	—	839	1	no	—
14	Q₁₆	D₈₃₉	1	1	yes	characteristic
15	C₁₆	—	839	1	no	—
16	Q₈	—	2	1	no	—
17	Q₈	—	1678	1	no	—
18	C₈	C₂×D₈₃₉	1	1	yes	characteristic
19	C₄	—	4	1	no	—
20	C₄	—	3356	1	no	—
21	C₄	C₂²⋊D₈₃₉	1	1	yes	characteristic
22	C₂	#27211940	1	1	yes	characteristic

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

N	H ≅ G/N	type
11. C₈₃₉	Q₃₂	semidirect

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