Subgroups — #37548890

Order 23168.

38 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26042118	C₂	1	2	yes	maximal, complemented
2	C₂×#19153722	C₂	1	1	yes	maximal, characteristic
3	#19153722	C₄	1	1	yes	characteristic
4	#19153722	C₂²	1	1	yes	characteristic
5	C₂×C₁₆×C₁₈₁	C₄	1	1	yes	characteristic
6	C₂×C₈×C₁₈₁	C₈	1	1	yes	characteristic
7	C₁₆×C₁₈₁	C₈	1	1	yes	characteristic
8	C₁₆×C₁₈₁	C₂×C₄	1	1	yes	characteristic
9	C₂×C₄×C₁₈₁	C₁₆	1	1	yes	characteristic
10	C₈×C₁₈₁	C₁₆	1	1	yes	characteristic
11	C₈×C₁₈₁	C₂×C₈	1	1	yes	characteristic
12	C₂²×C₁₈₁	C₃₂	1	1	yes	characteristic
13	C₄×C₁₈₁	C₃₂	1	1	yes	characteristic
14	C₄×C₁₈₁	C₂×C₁₆	1	1	yes	characteristic
15	C₂×C₁₈₁	—	2	1	no	—
16	C₂×C₁₈₁	C₂×C₃₂	1	1	yes	characteristic
17	C₁₈₁	M₁₂₈	1	1	yes	characteristic, complemented, Sylow
18	M₁₂₈	—	181	1	no	maximal, Sylow
19	C₂×C₃₂	—	181	1	no	—
20	C₆₄	—	181	2	no	—
21	C₂×C₁₆	#10624382	1	1	yes	characteristic
22	C₃₂	—	181	1	no	—
23	C₃₂	—	181	1	no	—
24	C₂×C₈	#13089685	1	1	yes	characteristic
25	C₁₆	#13089685	1	1	yes	characteristic
26	C₁₆	C₂×#10624382	1	1	yes	characteristic
27	C₂×C₄	#15668452	1	1	yes	characteristic
28	C₈	#15668452	1	1	yes	characteristic
29	C₈	C₂×#13089685	1	1	yes	characteristic
30	C₂²	#19153866	1	1	yes	characteristic
31	C₄	#19153866	1	1	yes	characteristic
32	C₄	C₂×#15668452	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	C₂×#19153866	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #26042118	C₂	semidirect
17. C₁₈₁	M₁₂₈	semidirect

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