Subgroups — #27212440

Order 13472.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20269774	C₂	1	2	yes	maximal, complemented
2	C₂×#16809890	C₂	1	1	yes	maximal, characteristic
3	#16809890	C₄	1	1	yes	characteristic
4	#16809890	C₂²	1	1	yes	characteristic
5	C₂×C₄×C₄₂₁	C₄	1	1	yes	characteristic
6	C₂²×C₄₂₁	C₈	1	1	yes	characteristic
7	C₄×C₄₂₁	C₈	1	1	yes	characteristic
8	C₄×C₄₂₁	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄₂₁	—	2	1	no	—
10	C₂×C₄₂₁	C₂×C₈	1	1	yes	characteristic
11	C₄₂₁	M₃₂	1	1	yes	characteristic, complemented, Sylow
12	M₃₂	—	421	1	no	maximal, Sylow
13	C₂×C₈	—	421	1	no	—
14	C₁₆	—	421	2	no	—
15	C₂×C₄	#13132997	1	1	yes	characteristic
16	C₈	—	421	1	no	—
17	C₈	—	421	1	no	—
18	C₂²	#16809897	1	1	yes	characteristic
19	C₄	#16809897	1	1	yes	characteristic
20	C₄	C₂×#13132997	1	1	yes	characteristic
21	C₂	—	2	1	no	—
22	C₂	C₂×#16809897	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #20269774	C₂	semidirect
11. C₄₂₁	M₃₂	semidirect

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