Subgroups — C₄⋊#16812365 #28357286

Order 13856.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16812365	C₂	1	2	yes	maximal
2	C₄×Dic₄₃₃	C₂	1	1	yes	maximal, characteristic
3	#16812365	—	2	2	no	—
4	C₂×Dic₄₃₃	C₄	1	1	yes	characteristic
5	C₂×Dic₄₃₃	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₄₃₃	C₄	1	1	yes	characteristic
7	C₂²×C₄₃₃	C₂×C₄	1	1	yes	characteristic
8	C₄×C₄₃₃	C₈	1	2	yes	complemented
9	Dic₄₃₃	—	2	1	no	—
10	Dic₄₃₃	D₄	1	1	yes	characteristic
11	Dic₄₃₃	Q₈	1	1	yes	characteristic
12	C₂×C₄₃₃	C₄⋊C₄	1	1	yes	characteristic
13	C₂×C₄₃₃	C₂×C₈	1	1	yes	characteristic
14	C₂×C₄₃₃	M₁₆	1	1	yes	characteristic
15	C₄₃₃	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
16	C₄⋊C₈	—	433	1	no	maximal, Sylow
17	C₂×C₈	—	433	2	no	—
18	C₄²	—	433	1	no	—
19	C₂×C₄	—	433	1	no	—
20	C₂×C₄	—	433	1	no	—
21	C₂×C₄	#13181884	1	1	yes	characteristic
22	C₈	—	866	2	no	—
23	C₂²	C₂×#13181884	1	1	yes	characteristic
24	C₄	—	866	1	no	—
25	C₄	—	433	1	no	—
26	C₄	—	433	1	no	—
27	C₄	#16812365	1	2	yes	complemented
28	C₂	C₄⋊#13181884	1	1	yes	characteristic
29	C₂	C₂×#16812365	1	1	yes	characteristic
30	C₂	#20294107	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.