Subgroups — #27212436

Order 13472.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20269781	C₂	1	2	yes	maximal
2	C₈×D₄₂₁	C₂	1	1	yes	maximal, characteristic
3	#16809897	—	2	2	no	—
4	C₄×D₄₂₁	C₂²	1	1	yes	characteristic
5	#16809890	C₄	1	1	yes	characteristic
6	C₈×C₄₂₁	C₄	1	1	yes	characteristic
7	C₂×D₄₂₁	Q₈	1	1	yes	characteristic
8	C₄×C₄₂₁	C₂×C₄	1	1	yes	characteristic
9	Dic₄₂₁	D₄	1	1	yes	characteristic
10	C₂×C₄₂₁	C₄⋊C₄	1	1	yes	characteristic
11	D₄₂₁	—	2	1	no	—
12	C₄₂₁	#108	1	1	yes	characteristic, complemented, Sylow
13	#108	—	421	1	no	maximal, Sylow
14	M₁₆	—	421	2	no	—
15	C₂×C₈	—	421	1	no	—
16	C₂×C₄	—	421	1	no	—
17	C₈	—	842	2	no	—
18	C₈	—	421	1	no	—
19	C₈	#13132997	1	1	yes	characteristic
20	C₂²	—	421	1	no	—
21	C₄	—	421	1	no	—
22	C₄	C₂×#13132997	1	1	yes	characteristic
23	C₂	—	842	1	no	—
24	C₂	C₄⋊#13132997	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. C₄₂₁	#108	semidirect

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