Subgroups — C₂²×#14272347 #21418633

Order 7456.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14272347	C₂	1	6	yes	maximal, direct product factor
2	C₂²×#11745400	C₂	1	1	yes	maximal, characteristic
3	#14272347	C₂²	1	4	yes	direct product factor
4	C₂×#11745400	C₄	1	3	yes	—
5	C₂×#11745400	C₂²	1	3	yes	—
6	C₂²×D₂₃₃	C₄	1	1	yes	characteristic
7	C₂²×C₂₃₃	C₈	1	1	yes	characteristic, complemented
8	C₂×D₂₃₃	C₈	1	3	yes	complemented
9	C₂×D₂₃₃	C₂×C₄	1	3	yes	—
10	#11745400	C₂×C₄	1	3	yes	—
11	#11745400	C₂³	1	1	yes	characteristic
12	C₂×C₂₃₃	C₂×C₈	1	3	yes	complemented
13	D₂₃₃	C₂×C₈	1	3	yes	complemented
14	D₂₃₃	C₂²×C₄	1	1	yes	characteristic
15	C₂₃₃	C₂²×C₈	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₈	—	233	1	no	maximal, Sylow
17	C₂²×C₄	—	233	1	no	—
18	C₂×C₈	—	233	6	no	—
19	C₂³	—	233	1	no	—
20	C₂×C₄	—	233	3	no	—
21	C₂×C₄	—	233	3	no	—
22	C₈	—	233	4	no	—
23	C₂²	—	233	3	no	—
24	C₂²	—	233	3	no	—
25	C₂²	#14272347	1	1	yes	characteristic, direct product factor
26	C₄	—	233	1	no	—
27	C₄	—	233	3	no	—
28	C₂	—	233	1	no	—
29	C₂	—	233	3	no	—
30	C₂	C₂×#14272347	1	3	yes	direct product factor

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