Subgroups — C₄×#19129199 #36342430

Order 21568.

58 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19129199	C₂	1	2	yes	maximal
2	C₄×#14582115	C₂	1	1	yes	maximal, characteristic
3	#19129199	C₄	1	4	yes	direct product factor
4	C₂×#14582115	C₄	1	1	yes	characteristic
5	C₂×#14582115	C₂²	1	1	yes	characteristic
6	C₄×#13062438	C₄	1	1	yes	characteristic
7	#14582115	C₈	1	2	yes	—
8	#14582115	C₂×C₄	1	2	yes	—
9	C₂×#13062438	C₈	1	1	yes	characteristic
10	C₂×#13062438	C₂×C₄	1	1	yes	characteristic
11	C₄×D₃₃₇	C₈	1	1	yes	characteristic
12	C₂×D₃₃₇	C₂×C₈	1	1	yes	characteristic
13	#13062438	C₁₆	1	2	yes	complemented
14	#13062438	C₄²	1	1	yes	characteristic
15	#13062438	C₂×C₈	1	1	yes	characteristic
16	C₄×C₃₃₇	C₁₆	1	1	yes	characteristic, complemented
17	Dic₃₃₇	C₁₆	1	1	yes	characteristic, complemented
18	C₂×C₃₃₇	C₂×C₁₆	1	1	yes	characteristic
19	D₃₃₇	C₄×C₈	1	1	yes	characteristic
20	D₃₃₇	C₂×C₁₆	1	1	yes	characteristic
21	C₃₃₇	C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
22	C₄×C₁₆	—	337	1	no	maximal, Sylow
23	C₂×C₁₆	—	337	2	no	—
24	C₄×C₈	—	337	1	no	—
25	C₂×C₈	—	337	1	no	—
26	C₂×C₈	—	337	1	no	—
27	C₄²	—	337	1	no	—
28	C₁₆	—	337	4	no	—
29	C₂×C₄	—	337	1	no	—
30	C₂×C₄	—	337	1	no	—
31	C₂×C₄	—	337	1	no	—
32	C₈	—	337	2	no	—
33	C₈	—	337	2	no	—
34	C₂²	—	337	1	no	—
35	C₄	—	337	1	no	—
36	C₄	—	337	1	no	—
37	C₄	—	337	2	no	—
38	C₄	—	337	1	no	—
39	C₄	#19129199	1	1	yes	characteristic, direct product factor
40	C₂	—	337	1	no	—
41	C₂	—	337	1	no	—
42	C₂	C₂×#19129199	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.