Subgroups — #37560355

Order 23872.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26045842	C₂	1	2	yes	maximal, complemented
2	C₁₆×D₃₇₃	C₂	1	1	yes	maximal, characteristic
3	C₈×D₃₇₃	C₄	1	1	yes	characteristic
4	#20238585	C₂²	1	1	yes	characteristic
5	C₁₆×C₃₇₃	C₄	1	1	yes	characteristic
6	C₄×D₃₇₃	C₈	1	1	yes	characteristic
7	#15688412	C₈	1	1	yes	characteristic
8	C₈×C₃₇₃	C₂×C₄	1	1	yes	characteristic
9	C₂×D₃₇₃	C₁₆	1	1	yes	characteristic
10	C₄×C₃₇₃	C₂×C₈	1	1	yes	characteristic
11	Dic₃₇₃	C₁₆	1	1	yes	characteristic
12	C₂×C₃₇₃	C₂×C₁₆	1	1	yes	characteristic
13	D₃₇₃	—	2	1	no	—
14	C₃₇₃	M₆₄	1	1	yes	characteristic, complemented, Sylow
15	M₆₄	—	373	1	no	maximal, Sylow
16	C₂×C₁₆	—	373	1	no	—
17	C₃₂	—	373	2	no	—
18	C₂×C₈	—	373	1	no	—
19	C₁₆	—	373	1	no	—
20	C₁₆	#13093637	1	1	yes	characteristic
21	C₂×C₄	—	373	1	no	—
22	C₈	—	373	1	no	—
23	C₈	C₂×#13093637	1	1	yes	characteristic
24	C₂²	—	373	1	no	—
25	C₄	—	373	1	no	—
26	C₄	D₃₇₃⋊C₈	1	1	yes	characteristic
27	C₂	—	746	1	no	—
28	C₂	D₃₇₃⋊C₁₆	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #26045842	C₂	semidirect
14. C₃₇₃	M₆₄	semidirect

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