Subgroups — #37560345

Order 23872.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26045866	C₂	1	2	yes	maximal
2	C₄×#15688412	C₂	1	1	yes	maximal, characteristic
3	#20238613	—	2	2	no	—
4	C₂×#15688412	C₄	1	1	yes	characteristic
5	C₂×#15688412	C₂²	1	1	yes	characteristic
6	C₄²×C₃₇₃	C₄	1	1	yes	characteristic
7	#15688412	C₈	1	2	yes	—
8	#15688412	D₄	1	1	yes	characteristic
9	#15688412	Q₈	1	1	yes	characteristic
10	C₂×C₄×C₃₇₃	—	2	1	no	—
11	C₂×C₄×C₃₇₃	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₃₇₃	M₁₆	1	1	yes	characteristic
13	C₄×C₃₇₃	—	2	2	no	—
14	C₄×C₃₇₃	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₃₇₃	C₂×C₈	1	1	yes	characteristic
16	C₂×C₃₇₃	—	2	1	no	—
17	C₂×C₃₇₃	C₄⋊C₈	1	1	yes	characteristic
18	C₃₇₃	#364	1	1	yes	characteristic, complemented, Sylow
19	#364	—	373	1	no	maximal, Sylow
20	M₃₂	—	373	2	no	—
21	C₄×C₈	—	373	1	no	—
22	C₂×C₈	—	373	1	no	—
23	C₂×C₈	—	373	1	no	—
24	C₄²	#13093637	1	1	yes	characteristic
25	C₁₆	—	746	2	no	—
26	C₂×C₄	—	2	1	no	—
27	C₂×C₄	C₂×#13093637	1	1	yes	characteristic
28	C₈	—	373	1	no	—
29	C₈	—	373	1	no	—
30	C₈	—	373	2	no	—
31	C₂²	#20238619	1	1	yes	characteristic
32	C₄	—	2	2	no	—
33	C₄	C₄⋊#13093637	1	1	yes	characteristic
34	C₄	D₃₇₃⋊C₈	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#26045859	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₃₇₃	#364	semidirect

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