Subgroups — C₂×#16836603 #21418619

Order 7456.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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