Subgroups — #37554009

Order 23488.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26044197	C₂	1	1	yes	maximal, characteristic
2	#26044193	C₂	1	1	yes	maximal, characteristic
3	M₃₂×C₃₆₇	C₂	1	1	yes	maximal, characteristic
4	#19154561	—	2	1	no	—
5	C₄⋊Dic₃₆₇	—	2	1	no	—
6	C₂×C₈×C₃₆₇	C₂²	1	1	yes	characteristic
7	C₁₆×C₃₆₇	C₄	1	2	yes	complemented
8	C₂×Dic₃₆₇	—	4	1	no	—
9	C₃₆₇⋊C₈	—	4	1	no	—
10	C₂×C₄×C₃₆₇	D₄	1	1	yes	characteristic
11	C₈×C₃₆₇	C₂×C₄	1	1	yes	characteristic
12	C₈×C₃₆₇	Q₈	1	1	yes	characteristic
13	C₂²×C₃₆₇	SD₁₆	1	1	yes	characteristic
14	C₄×C₃₆₇	C₄⋊C₄	1	1	yes	characteristic
15	C₄×C₃₆₇	SD₁₆	1	1	yes	characteristic
16	Dic₃₆₇	—	8	1	no	—
17	C₂×C₃₆₇	—	2	1	no	—
18	C₂×C₃₆₇	#106	1	1	yes	characteristic
19	C₃₆₇	#365	1	1	yes	characteristic, complemented, Sylow
20	#365	—	367	1	no	maximal, Sylow
21	M₃₂	D₃₆₇	1	1	yes	characteristic
22	#108	—	367	1	no	—
23	#106	—	367	1	no	—
24	M₁₆	—	734	1	no	—
25	C₂×C₈	C₂×D₃₆₇	1	1	yes	characteristic
26	C₄⋊C₄	—	734	1	no	—
27	C₁₆	Dic₃₆₇	1	2	yes	complemented
28	C₂×C₄	—	1468	1	no	—
29	C₂×C₄	D₁₄₆₈	1	1	yes	characteristic
30	C₈	—	1468	1	no	—
31	C₈	C₂×Dic₃₆₇	1	1	yes	characteristic
32	C₈	Dic₇₃₄	1	1	yes	characteristic
33	C₂²	#19154566	1	1	yes	characteristic
34	C₄	—	2936	1	no	—
35	C₄	C₄⋊Dic₃₆₇	1	1	yes	characteristic
36	C₄	#19154566	1	1	yes	characteristic
37	C₂	—	2	1	no	—
38	C₂	#26044193	1	1	yes	characteristic

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

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