Subgroups — C₂²×#10596927 #14558586

Order 2368.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10596927	C₂	1	6	yes	maximal, direct product factor
2	C₂²×#64436	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄×C₃₇	C₄	1	1	yes	characteristic
4	C₂×#64436	C₄	1	3	yes	—
5	C₂×#64436	C₂²	1	3	yes	—
6	#10596927	C₂²	1	4	yes	direct product factor
7	C₂³×C₃₇	C₈	1	1	yes	characteristic
8	C₂×C₄×C₃₇	C₈	1	3	yes	—
9	C₂×C₄×C₃₇	C₂×C₄	1	3	yes	—
10	#64436	C₂×C₄	1	3	yes	—
11	#64436	C₂³	1	1	yes	characteristic
12	C₂²×C₃₇	C₁₆	1	4	yes	complemented
13	C₂²×C₃₇	C₂×C₈	1	3	yes	—
14	C₄×C₃₇	C₂×C₈	1	3	yes	—
15	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
16	C₂×C₃₇	C₂×C₁₆	1	6	yes	complemented
17	C₂×C₃₇	C₂²×C₈	1	1	yes	characteristic
18	C₂²×C₁₆	—	37	1	no	maximal, Sylow
19	C₃₇	C₂²×C₁₆	1	1	yes	characteristic, complemented, Sylow
20	C₂²×C₈	—	37	1	no	—
21	C₂×C₁₆	—	37	6	no	—
22	C₂²×C₄	#3866	1	1	yes	characteristic
23	C₂×C₈	—	37	3	no	—
24	C₂×C₈	—	37	3	no	—
25	C₁₆	—	37	4	no	—
26	C₂³	#64438	1	1	yes	characteristic
27	C₂×C₄	#64438	1	3	yes	—
28	C₂×C₄	C₂×#3866	1	3	yes	—
29	C₈	—	37	1	no	—
30	C₈	—	37	3	no	—
31	C₂²	#10596927	1	4	yes	direct product factor
32	C₂²	C₂×#64438	1	3	yes	—
33	C₄	C₂×#64438	1	3	yes	—
34	C₄	C₂²×#3866	1	1	yes	characteristic
35	C₂	C₂×#10596927	1	6	yes	direct product factor
36	C₂	C₂²×#64438	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.