Subgroups — #37565073

Order 24256.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃₇₉⋊C₁₆	C₂	1	1	yes	maximal, characteristic
2	#27131267	C₂	1	1	yes	maximal, characteristic
3	#108×C₃₇₉	C₂	1	1	yes	maximal, characteristic
4	#20258590	—	2	1	no	—
5	C₃₇₉⋊C₁₆	C₄	1	2	yes	—
6	M₁₆×C₃₇₉	—	2	1	no	—
7	C₂×C₈×C₃₇₉	C₂²	1	1	yes	characteristic
8	C₃₇₉⋊C₈	—	4	1	no	—
9	C₂×C₄×C₃₇₉	D₄	1	1	yes	characteristic
10	C₈×C₃₇₉	—	4	1	no	—
11	C₈×C₃₇₉	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₇₉	Q₈	1	1	yes	characteristic
13	C₂²×C₃₇₉	Q₁₆	1	1	yes	characteristic
14	C₄×C₃₇₉	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₃₇₉	D₈	1	1	yes	characteristic
16	C₂×C₃₇₉	—	2	1	no	—
17	C₂×C₃₇₉	#107	1	1	yes	characteristic
18	C₃₇₉	#368	1	1	yes	characteristic, complemented, Sylow
19	#368	—	379	1	no	maximal, Sylow
20	C₂×C₁₆	—	379	1	no	—
21	#108	—	379	1	no	—
22	#108	D₃₇₉	1	1	yes	characteristic
23	M₁₆	—	2	1	no	—
24	M₁₆	—	758	1	no	—
25	C₂×C₈	C₂×D₃₇₉	1	1	yes	characteristic
26	C₁₆	—	379	2	no	—
27	C₂×C₄	C₂²⋊D₃₇₉	1	1	yes	characteristic
28	C₈	—	4	1	no	—
29	C₈	—	1516	1	no	—
30	C₈	C₄×D₃₇₉	1	1	yes	characteristic
31	C₈	Dic₇₅₈	1	1	yes	characteristic
32	C₂²	#20258596	1	1	yes	characteristic
33	C₄	Dic₃₇₉⋊C₄	1	1	yes	characteristic
34	C₄	#20258591	1	1	yes	characteristic
35	C₂	—	2	1	no	—
36	C₂	#27131264	1	1	yes	characteristic

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

N	H ≅ G/N	type
18. C₃₇₉	#368	semidirect

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