Subgroups — #14558591

Order 2368.

84 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11924610	C₂	1	3	yes	maximal, complemented
2	C₂×#10596927	C₂	1	3	yes	maximal, complemented
3	#11924543	C₂	1	1	yes	maximal, characteristic
4	#41×C₃₇	C₄	1	1	yes	characteristic
5	#10596934	C₄	1	3	yes	—
6	C₂×#64436	C₂²	1	3	yes	—
7	#10596927	C₂²	1	1	yes	characteristic
8	#10596927	C₂²	1	3	yes	—
9	Q₈×C₃₇	C₈	1	1	yes	characteristic
10	D₄×C₃₇	C₈	1	3	yes	—
11	C₂×C₄×C₃₇	C₂×C₄	1	3	yes	—
12	#64436	C₂×C₄	1	3	yes	—
13	#64436	C₂³	1	1	yes	characteristic
14	C₂²×C₃₇	C₂×C₈	1	3	yes	—
15	C₄×C₃₇	C₂×C₈	1	3	yes	—
16	C₄×C₃₇	C₂²×C₄	1	1	yes	characteristic
17	C₂×C₃₇	—	2	3	no	—
18	C₂×C₃₇	C₂²×C₈	1	1	yes	characteristic
19	#504	—	37	1	no	maximal, Sylow
20	C₃₇	#504	1	1	yes	characteristic, complemented, Sylow
21	#131	—	37	1	no	—
22	M₃₂	—	37	3	no	—
23	C₂×C₁₆	—	37	3	no	—
24	#41	#3866	1	1	yes	characteristic
25	M₁₆	—	37	3	no	—
26	C₂×C₈	—	37	3	no	—
27	C₁₆	—	37	1	no	—
28	C₁₆	—	37	3	no	—
29	Q₈	#64438	1	1	yes	characteristic
30	D₄	#64438	1	3	yes	—
31	C₂×C₄	C₂×#3866	1	3	yes	—
32	C₈	—	37	1	no	—
33	C₈	—	37	3	no	—
34	C₂²	C₂×#64438	1	3	yes	—
35	C₄	C₂×#64438	1	3	yes	—
36	C₄	C₂²×#3866	1	1	yes	characteristic
37	C₂	—	2	3	no	—
38	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.