Subgroups — C₂×#24925049 #36342411

Order 21568.

34 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24925049	C₂	1	2	yes	maximal, direct product factor
2	C₂×#19129188	C₂	1	1	yes	maximal, characteristic
3	#19129188	C₄	1	1	yes	characteristic
4	#19129188	C₂²	1	1	yes	characteristic
5	C₂×#14582106	C₄	1	1	yes	characteristic
6	#14582106	C₈	1	1	yes	characteristic
7	#14582106	C₂×C₄	1	1	yes	characteristic
8	C₂×C₄×C₃₃₇	C₈	1	1	yes	characteristic
9	C₂²×C₃₃₇	C₁₆	1	1	yes	characteristic
10	C₄×C₃₃₇	C₁₆	1	1	yes	characteristic
11	C₄×C₃₃₇	C₂×C₈	1	1	yes	characteristic
12	C₂×C₃₃₇	C₃₂	1	2	yes	complemented
13	C₂×C₃₃₇	C₂×C₁₆	1	1	yes	characteristic
14	C₃₃₇	C₂×C₃₂	1	1	yes	characteristic, complemented, Sylow
15	C₂×C₃₂	—	337	1	no	maximal, Sylow
16	C₂×C₁₆	—	337	1	no	—
17	C₃₂	—	337	2	no	—
18	C₂×C₈	—	337	1	no	—
19	C₁₆	—	337	1	no	—
20	C₁₆	—	337	1	no	—
21	C₂×C₄	#14582115	1	1	yes	characteristic
22	C₈	—	337	1	no	—
23	C₈	—	337	1	no	—
24	C₂²	#19129197	1	1	yes	characteristic
25	C₄	#19129197	1	1	yes	characteristic
26	C₄	C₂×#14582115	1	1	yes	characteristic
27	C₂	#24925049	1	2	yes	direct product factor
28	C₂	C₂×#19129197	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.