Subgroups — #17992798

Order 4736.

56 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14557359	C₂	1	2	yes	maximal
2	C₂×C₃₂×C₃₇	C₂	1	1	yes	maximal, characteristic
3	#11924470	—	2	2	no	—
4	C₂×C₁₆×C₃₇	C₂²	1	1	yes	characteristic
5	C₃₂×C₃₇	C₄	1	2	yes	complemented
6	C₂×C₈×C₃₇	D₄	1	1	yes	characteristic
7	C₄⋊Dic₃₇	—	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	C₂×Dic₃₇	—	8	2	no	—
12	C₈×C₃₇	C₄⋊C₄	1	1	yes	characteristic
13	C₈×C₃₇	Q₁₆	1	1	yes	characteristic
14	C₂²×C₃₇	D₁₆	1	1	yes	characteristic
15	C₄×C₃₇	#107	1	1	yes	characteristic
16	C₄×C₃₇	Q₃₂	1	1	yes	characteristic
17	Dic₃₇	—	16	2	no	—
18	#1424	—	37	1	no	maximal, Sylow
19	C₂×C₃₇	#366	1	1	yes	characteristic
20	C₂×C₃₇	SD₆₄	1	2	yes	—
21	C₂×C₃₂	D₃₇	1	1	yes	characteristic
22	#366	—	37	2	no	—
23	C₃₇	#1424	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₁₆	C₂×D₃₇	1	1	yes	characteristic
25	#107	—	74	2	no	—
26	C₃₂	Dic₃₇	1	2	yes	complemented
27	C₂×C₈	D₁₄₈	1	1	yes	characteristic
28	C₄⋊C₄	—	148	2	no	—
29	C₁₆	Dic₇₄	1	1	yes	characteristic
30	C₁₆	C₂×Dic₃₇	1	1	yes	characteristic
31	C₂×C₄	—	296	2	no	—
32	C₂×C₄	D₂₉₆	1	1	yes	characteristic
33	C₈	Dic₁₄₈	1	1	yes	characteristic
34	C₈	C₄⋊Dic₃₇	1	1	yes	characteristic
35	C₂²	D₅₉₂	1	1	yes	characteristic
36	C₄	—	592	2	no	—
37	C₄	#11924470	1	1	yes	characteristic
38	C₄	Dic₂₉₆	1	1	yes	characteristic
39	C₂	#14557359	1	1	yes	characteristic
40	C₂	#14557372	1	2	yes	—

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.