Subgroups — #36342394

Order 21568.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#14582115	C₂	1	2	yes	maximal
2	C₈×#13062438	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582115	—	2	2	no	—
4	#19129193	C₄	1	1	yes	characteristic
5	C₄×#13062438	C₂²	1	1	yes	characteristic
6	C₈×D₃₃₇	C₄	1	1	yes	characteristic
7	#14582115	—	4	2	no	—
8	C₂×#13062438	D₄	1	1	yes	characteristic
9	C₂×#13062438	Q₈	1	1	yes	characteristic
10	#14582113	—	2	1	no	—
11	C₄×D₃₃₇	C₂×C₄	1	1	yes	characteristic
12	#14582106	C₈	1	1	yes	characteristic, complemented
13	C₈×C₃₃₇	C₈	1	1	yes	characteristic, complemented
14	C₂×D₃₃₇	C₄⋊C₄	1	1	yes	characteristic
15	#13062438	—	2	1	no	—
16	#13062438	SD₁₆	1	2	yes	—
17	C₄×C₃₃₇	C₂×C₈	1	1	yes	characteristic
18	Dic₃₃₇	M₁₆	1	1	yes	characteristic
19	C₂×C₃₃₇	C₄⋊C₈	1	1	yes	characteristic
20	D₃₃₇	#106	1	1	yes	characteristic
21	D₃₃₇	#108	1	1	yes	characteristic
22	C₃₃₇	#334	1	1	yes	characteristic, complemented, Sylow
23	#334	—	337	1	no	maximal, Sylow
24	C₄⋊C₈	—	337	2	no	—
25	C₄×C₈	—	337	1	no	—
26	C₂×C₈	—	337	1	no	—
27	C₂×C₈	—	337	1	no	—
28	C₂×C₈	—	674	2	no	—
29	C₄²	—	337	1	no	—
30	C₂×C₄	—	337	1	no	—
31	C₂×C₄	—	337	1	no	—
32	C₂×C₄	—	337	1	no	—
33	C₈	—	1348	2	no	—
34	C₈	—	337	1	no	—
35	C₈	—	674	1	no	—
36	C₈	#14582115	1	1	yes	characteristic, complemented
37	C₂²	—	337	1	no	—
38	C₄	—	337	2	no	—
39	C₄	—	337	1	no	—
40	C₄	—	674	1	no	—
41	C₄	C₂×#14582115	1	1	yes	characteristic
42	C₂	—	337	1	no	—
43	C₂	—	337	1	no	—
44	C₂	C₄⋊#14582115	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.