Subgroups — C₂²×#16836606 #28417551

Order 14912.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16836606	C₂	1	6	yes	maximal, direct product factor
2	C₂²×#14272345	C₂	1	1	yes	maximal, characteristic
3	#16836606	C₂²	1	4	yes	direct product factor
4	C₂×#14272345	C₄	1	3	yes	—
5	C₂×#14272345	C₂²	1	3	yes	—
6	C₂²×Dic₂₃₃	C₄	1	1	yes	characteristic
7	#14272345	C₂×C₄	1	3	yes	—
8	#14272345	C₂³	1	1	yes	characteristic
9	C₂×Dic₂₃₃	C₈	1	3	yes	—
10	C₂×Dic₂₃₃	C₂×C₄	1	3	yes	—
11	C₂³×C₂₃₃	C₈	1	1	yes	characteristic
12	C₂²×C₂₃₃	C₁₆	1	4	yes	complemented
13	C₂²×C₂₃₃	C₂×C₈	1	3	yes	—
14	Dic₂₃₃	C₂×C₈	1	3	yes	—
15	Dic₂₃₃	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₂₃₃	C₂×C₁₆	1	6	yes	complemented
17	C₂×C₂₃₃	C₂²×C₈	1	1	yes	characteristic
18	C₂₃₃	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
19	C₂²×C₁₆	—	233	1	no	maximal, Sylow
20	C₂²×C₈	—	233	1	no	—
21	C₂×C₁₆	—	233	6	no	—
22	C₂²×C₄	—	233	1	no	—
23	C₂×C₈	—	233	3	no	—
24	C₂×C₈	—	233	3	no	—
25	C₁₆	—	233	4	no	—
26	C₂³	#14272347	1	1	yes	characteristic
27	C₂×C₄	—	233	3	no	—
28	C₂×C₄	—	233	3	no	—
29	C₈	—	233	1	no	—
30	C₈	—	233	3	no	—
31	C₂²	#16836606	1	4	yes	direct product factor
32	C₂²	C₂×#14272347	1	3	yes	—
33	C₄	—	233	1	no	—
34	C₄	—	233	3	no	—
35	C₂	C₂×#16836606	1	6	yes	direct product factor
36	C₂	C₂²×#14272347	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.