Subgroups — C₂²⋊#14272345 #21418591

Order 7456.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14272345	C₂	1	2	yes	maximal, complemented
2	C₂²×Dic₂₃₃	C₂	1	1	yes	maximal, characteristic
3	#14272345	—	2	2	no	—
4	C₂×Dic₂₃₃	—	2	2	no	—
5	C₂×Dic₂₃₃	C₄	1	1	yes	characteristic
6	C₂×Dic₂₃₃	C₂²	1	1	yes	characteristic
7	C₂³×C₂₃₃	C₄	1	1	yes	characteristic
8	C₂²×C₂₃₃	—	2	1	no	—
9	C₂²×C₂₃₃	—	2	1	no	—
10	C₂²×C₂₃₃	C₈	1	2	yes	complemented
11	C₂²×C₂₃₃	C₂×C₄	1	1	yes	characteristic
12	Dic₂₃₃	—	2	1	no	—
13	Dic₂₃₃	D₄	1	2	yes	—
14	C₂×C₂₃₃	—	2	2	no	—
15	C₂×C₂₃₃	C₂²⋊C₄	1	1	yes	characteristic
16	C₂×C₂₃₃	C₂×C₈	1	1	yes	characteristic
17	C₂×C₂₃₃	M₁₆	1	1	yes	characteristic
18	C₂₃₃	C₂²⋊C₈	1	1	yes	characteristic, complemented, Sylow
19	C₂²⋊C₈	—	233	1	no	maximal, Sylow
20	C₂²×C₄	—	233	1	no	—
21	C₂×C₈	—	233	2	no	—
22	C₂³	#11745400	1	1	yes	characteristic
23	C₂×C₄	—	466	2	no	—
24	C₂×C₄	—	233	1	no	—
25	C₂×C₄	—	233	1	no	—
26	C₈	—	466	2	no	—
27	C₂²	—	2	1	no	—
28	C₂²	—	2	1	no	—
29	C₂²	#14272345	1	2	yes	complemented
30	C₂²	C₂×#11745400	1	1	yes	characteristic
31	C₄	—	466	1	no	—
32	C₄	—	233	2	no	—
33	C₂	—	2	2	no	—
34	C₂	C₂²⋊#11745400	1	1	yes	characteristic
35	C₂	C₂×#14272345	1	1	yes	characteristic
36	C₂	#16836603	1	1	yes	characteristic

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