Subgroups — C₄⋊#16809897 #27212432

Order 13472.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16809897	C₂	1	2	yes	maximal
2	C₄×Dic₄₂₁	C₂	1	1	yes	maximal, characteristic
3	#16809897	—	2	2	no	—
4	C₂×Dic₄₂₁	C₄	1	1	yes	characteristic
5	C₂×Dic₄₂₁	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₄₂₁	C₄	1	1	yes	characteristic
7	C₂²×C₄₂₁	C₂×C₄	1	1	yes	characteristic
8	C₄×C₄₂₁	C₈	1	2	yes	complemented
9	Dic₄₂₁	—	2	1	no	—
10	Dic₄₂₁	D₄	1	1	yes	characteristic
11	Dic₄₂₁	Q₈	1	1	yes	characteristic
12	C₂×C₄₂₁	C₄⋊C₄	1	1	yes	characteristic
13	C₂×C₄₂₁	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄₂₁	M₁₆	1	1	yes	characteristic
15	C₄₂₁	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
16	C₄⋊C₈	—	421	1	no	maximal, Sylow
17	C₂×C₈	—	421	2	no	—
18	C₄²	—	421	1	no	—
19	C₂×C₄	—	421	1	no	—
20	C₂×C₄	—	421	1	no	—
21	C₂×C₄	#13132997	1	1	yes	characteristic
22	C₈	—	842	2	no	—
23	C₂²	C₂×#13132997	1	1	yes	characteristic
24	C₄	—	842	1	no	—
25	C₄	—	421	1	no	—
26	C₄	—	421	1	no	—
27	C₄	#16809897	1	2	yes	complemented
28	C₂	C₄⋊#13132997	1	1	yes	characteristic
29	C₂	C₂×#16809897	1	1	yes	characteristic
30	C₂	#20269781	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.