Subgroups — C₄⋊#14272345 #21418601

Order 7456.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14272345	C₂	1	2	yes	maximal
2	C₄×Dic₂₃₃	C₂	1	1	yes	maximal, characteristic
3	#14272345	—	2	2	no	—
4	C₂×Dic₂₃₃	C₄	1	1	yes	characteristic
5	C₂×Dic₂₃₃	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₂₃₃	C₄	1	1	yes	characteristic
7	C₂²×C₂₃₃	C₂×C₄	1	1	yes	characteristic
8	C₄×C₂₃₃	C₈	1	2	yes	complemented
9	Dic₂₃₃	—	2	1	no	—
10	Dic₂₃₃	D₄	1	1	yes	characteristic
11	Dic₂₃₃	Q₈	1	1	yes	characteristic
12	C₂×C₂₃₃	C₄⋊C₄	1	1	yes	characteristic
13	C₂×C₂₃₃	C₂×C₈	1	1	yes	characteristic
14	C₂×C₂₃₃	M₁₆	1	1	yes	characteristic
15	C₂₃₃	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
16	C₄⋊C₈	—	233	1	no	maximal, Sylow
17	C₂×C₈	—	233	2	no	—
18	C₄²	—	233	1	no	—
19	C₂×C₄	—	233	1	no	—
20	C₂×C₄	—	233	1	no	—
21	C₂×C₄	#11745400	1	1	yes	characteristic
22	C₈	—	466	2	no	—
23	C₂²	C₂×#11745400	1	1	yes	characteristic
24	C₄	—	466	1	no	—
25	C₄	—	233	1	no	—
26	C₄	—	233	1	no	—
27	C₄	#14272345	1	2	yes	complemented
28	C₂	C₄⋊#11745400	1	1	yes	characteristic
29	C₂	C₂×#14272345	1	1	yes	characteristic
30	C₂	#16836604	1	1	yes	characteristic

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