Subgroups — C₂×#20263740 #27163180

Order 12704.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20263740	C₂	1	4	yes	maximal, direct product factor
2	C₂×#15691794	C₂	1	2	yes	maximal, complemented
3	C₂²×Dic₃₉₇	C₂	1	1	yes	maximal, characteristic
4	#15691794	C₂²	1	4	yes	complemented
5	C₂×Dic₃₉₇	C₄	1	2	yes	—
6	C₂×Dic₃₉₇	C₄	1	1	yes	characteristic
7	C₂×Dic₃₉₇	C₂²	1	1	yes	characteristic
8	C₂×Dic₃₉₇	C₂²	1	2	yes	—
9	C₂³×C₃₉₇	C₄	1	1	yes	characteristic
10	C₂²×C₃₉₇	—	2	2	no	—
11	C₂²×C₃₉₇	C₂×C₄	1	2	yes	—
12	C₂²×C₃₉₇	C₂×C₄	1	1	yes	characteristic
13	Dic₃₉₇	C₂×C₄	1	1	yes	characteristic
14	Dic₃₉₇	C₂×C₄	1	2	yes	—
15	Dic₃₉₇	C₂³	1	1	yes	characteristic
16	C₂×C₃₉₇	—	2	2	no	—
17	C₂×C₃₉₇	M₁₆	1	2	yes	complemented
18	C₂×C₃₉₇	C₂²×C₄	1	1	yes	characteristic
19	C₃₉₇	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
20	C₂×M₁₆	—	397	1	no	maximal, Sylow
21	C₂²×C₄	—	397	1	no	—
22	M₁₆	—	397	4	no	—
23	C₂×C₈	—	397	2	no	—
24	C₂³	#13097544	1	1	yes	characteristic
25	C₂×C₄	—	397	2	no	—
26	C₂×C₄	—	397	2	no	—
27	C₂×C₄	—	397	1	no	—
28	C₂×C₄	—	397	1	no	—
29	C₈	—	397	4	no	—
30	C₂²	—	2	2	no	—
31	C₂²	C₂×#13097544	1	2	yes	—
32	C₂²	C₂×#13097544	1	1	yes	characteristic
33	C₄	—	397	1	no	—
34	C₄	—	397	1	no	—
35	C₄	—	397	2	no	—
36	C₂	—	2	2	no	—
37	C₂	#20263740	1	2	yes	direct product factor
38	C₂	C₂²×#13097544	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.