Subgroups — #17992800

Order 4736.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557363	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₃₇	C₂	1	1	yes	maximal, characteristic
3	#11924472	—	2	2	no	—
4	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
5	C₃₂×C₃₇	C₄	1	2	yes	—
6	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
7	#10596934	—	4	2	no	—
8	C₁₆×C₃₇	C₂×C₄	1	1	yes	characteristic
9	C₁₆×C₃₇	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₃₇	D₈	1	1	yes	characteristic
11	C₈×C₃₇	C₄⋊C₄	1	1	yes	characteristic
12	C₈×C₃₇	Q₁₆	1	1	yes	characteristic
13	#64436	—	8	2	no	—
14	C₂²×C₃₇	Q₃₂	1	1	yes	characteristic
15	C₄×C₃₇	#107	1	1	yes	characteristic
16	C₄×C₃₇	D₁₆	1	1	yes	characteristic
17	#1425	—	37	1	no	maximal, Sylow
18	C₂×C₃₇	—	2	1	no	—
19	C₂×C₃₇	#366	1	1	yes	characteristic
20	C₂×C₃₂	D₃₇	1	1	yes	characteristic
21	#368	—	37	2	no	—
22	C₃₇	#1425	1	1	yes	characteristic, complemented, Sylow
23	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
24	#108	—	74	2	no	—
25	C₃₂	Dic₃₇	1	2	yes	—
26	M₁₆	—	148	2	no	—
27	C₂×C₈	D₁₄₈	1	1	yes	characteristic
28	C₁₆	Dic₇₄	1	1	yes	characteristic
29	C₁₆	C₂×Dic₃₇	1	1	yes	characteristic
30	C₂×C₄	D₂₉₆	1	1	yes	characteristic
31	C₈	—	296	2	no	—
32	C₈	Dic₁₄₈	1	1	yes	characteristic
33	C₈	C₄⋊Dic₃₇	1	1	yes	characteristic
34	C₂²	Dic₂₉₆	1	1	yes	characteristic
35	C₄	#11924470	1	1	yes	characteristic
36	C₄	D₅₉₂	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#14557359	1	1	yes	characteristic

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

N	H ≅ G/N	type
22. C₃₇	#1425	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.