Subgroups — #37548885

Order 23168.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042207	C₂	1	2	yes	maximal
2	C₃₂×D₁₈₁	C₂	1	1	yes	maximal, characteristic
3	#19153887	—	2	2	no	—
4	C₁₆×D₁₈₁	C₂²	1	1	yes	characteristic
5	#19153722	C₄	1	1	yes	characteristic
6	C₃₂×C₁₈₁	C₄	1	1	yes	characteristic
7	#15668459	—	4	2	no	—
8	C₈×D₁₈₁	D₄	1	1	yes	characteristic
9	#15668424	Q₈	1	1	yes	characteristic
10	C₁₆×C₁₈₁	C₂×C₄	1	1	yes	characteristic
11	#13089685	—	8	2	no	—
12	C₄×D₁₈₁	D₈	1	1	yes	characteristic
13	#13089678	Q₁₆	1	1	yes	characteristic
14	C₈×C₁₈₁	C₄⋊C₄	1	1	yes	characteristic
15	C₂×D₁₈₁	Q₃₂	1	1	yes	characteristic
16	C₄×C₁₈₁	#107	1	1	yes	characteristic
17	Dic₁₈₁	D₁₆	1	1	yes	characteristic
18	C₂×C₁₈₁	#366	1	1	yes	characteristic
19	D₁₈₁	—	2	1	no	—
20	C₁₈₁	#1425	1	1	yes	characteristic, complemented, Sylow
21	#1425	—	181	1	no	maximal, Sylow
22	C₂×C₃₂	—	181	1	no	—
23	#368	—	181	2	no	—
24	C₂×C₁₆	—	181	1	no	—
25	#108	—	362	2	no	—
26	C₃₂	—	181	1	no	—
27	C₃₂	#10624382	1	1	yes	characteristic
28	M₁₆	—	724	2	no	—
29	C₂×C₈	—	181	1	no	—
30	C₁₆	—	181	1	no	—
31	C₁₆	C₂×#10624382	1	1	yes	characteristic
32	C₂×C₄	—	181	1	no	—
33	C₈	—	1448	2	no	—
34	C₈	—	181	1	no	—
35	C₈	C₄⋊#10624382	1	1	yes	characteristic
36	C₂²	—	181	1	no	—
37	C₄	—	181	1	no	—
38	C₄	#19153885	1	1	yes	characteristic
39	C₂	—	362	1	no	—
40	C₂	#26042205	1	1	yes	characteristic

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

N	H ≅ G/N	type
20. C₁₈₁	#1425	semidirect

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