Subgroups — #36342230

Order 21568.

42 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24925029	C₂	1	1	yes	maximal, characteristic
2	#24925027	C₂	1	1	yes	maximal, characteristic
3	#24924898	C₂	1	1	yes	maximal, characteristic
4	#19129195	—	2	1	no	—
5	C₄⋊#13062438	—	2	1	no	—
6	C₈×D₃₃₇	C₂²	1	1	yes	characteristic
7	#19129160	C₄	1	1	yes	characteristic, complemented
8	C₁₆×C₃₃₇	C₄	1	1	yes	characteristic, complemented
9	C₂×#13062438	—	4	1	no	—
10	#14582113	—	4	1	no	—
11	C₄×D₃₃₇	D₄	1	1	yes	characteristic
12	#14582106	Q₈	1	1	yes	characteristic
13	C₈×C₃₃₇	C₂×C₄	1	1	yes	characteristic
14	C₂×D₃₃₇	SD₁₆	1	1	yes	characteristic
15	#13062438	—	8	1	no	—
16	C₄×C₃₃₇	C₄⋊C₄	1	1	yes	characteristic
17	Dic₃₃₇	SD₁₆	1	1	yes	characteristic
18	C₂×C₃₃₇	#106	1	1	yes	characteristic
19	D₃₃₇	—	2	1	no	—
20	C₃₃₇	#365	1	1	yes	characteristic, complemented, Sylow
21	#365	—	337	1	no	maximal, Sylow
22	M₃₂	—	337	1	no	—
23	#108	—	337	1	no	—
24	#106	—	337	1	no	—
25	M₁₆	—	674	1	no	—
26	C₂×C₈	—	337	1	no	—
27	C₄⋊C₄	—	674	1	no	—
28	C₁₆	—	337	1	no	—
29	C₁₆	#13062438	1	1	yes	characteristic, complemented
30	C₂×C₄	—	1348	1	no	—
31	C₂×C₄	—	337	1	no	—
32	C₈	—	1348	1	no	—
33	C₈	—	337	1	no	—
34	C₈	C₂×#13062438	1	1	yes	characteristic
35	C₂²	—	337	1	no	—
36	C₄	—	337	1	no	—
37	C₄	—	2696	1	no	—
38	C₄	C₄⋊#13062438	1	1	yes	characteristic
39	C₂	—	674	1	no	—
40	C₂	#24925027	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.