Subgroups — #37559244

Order 23872.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26045732	C₂	1	1	yes	maximal, characteristic
2	#26045728	C₂	1	1	yes	maximal, characteristic
3	#106×C₃₇₃	C₂	1	1	yes	maximal, characteristic
4	#20238594	—	2	1	no	—
5	#20238585	C₄	1	2	yes	complemented
6	C₂×C₈×C₃₇₃	C₂²	1	1	yes	characteristic
7	C₄⋊C₄×C₃₇₃	—	2	1	no	—
8	#15688412	—	4	1	no	—
9	C₂×C₄×C₃₇₃	—	4	1	no	—
10	C₂×C₄×C₃₇₃	D₄	1	1	yes	characteristic
11	C₈×C₃₇₃	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₇₃	Q₈	1	1	yes	characteristic
13	C₂²×C₃₇₃	SD₁₆	1	1	yes	characteristic
14	C₄×C₃₇₃	—	8	1	no	—
15	C₄×C₃₇₃	C₄⋊C₄	1	1	yes	characteristic
16	C₄×C₃₇₃	SD₁₆	1	1	yes	characteristic
17	C₂×C₃₇₃	—	2	1	no	—
18	C₂×C₃₇₃	#106	1	1	yes	characteristic
19	C₃₇₃	#365	1	1	yes	characteristic, complemented, Sylow
20	#365	—	373	1	no	maximal, Sylow
21	M₃₂	—	373	1	no	—
22	#108	—	373	1	no	—
23	#106	D₃₇₃	1	1	yes	characteristic
24	M₁₆	—	746	1	no	—
25	C₂×C₈	C₂×D₃₇₃	1	1	yes	characteristic
26	C₄⋊C₄	—	2	1	no	—
27	C₁₆	—	373	2	no	—
28	C₂×C₄	—	4	1	no	—
29	C₂×C₄	C₂²⋊D₃₇₃	1	1	yes	characteristic
30	C₈	—	1492	1	no	—
31	C₈	C₄×D₃₇₃	1	1	yes	characteristic
32	C₈	Dic₇₄₆	1	1	yes	characteristic
33	C₂²	#20238598	1	1	yes	characteristic
34	C₄	—	8	1	no	—
35	C₄	#20238589	1	1	yes	characteristic
36	C₄	#20238597	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#26045723	1	1	yes	characteristic

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

N	H ≅ G/N	type
5. #20238585	C₄	semidirect
19. C₃₇₃	#365	semidirect

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