Subgroups — C₄×#15691794 #27163149

Order 12704.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15691794	C₂	1	2	yes	maximal
2	C₄×Dic₃₉₇	C₂	1	1	yes	maximal, characteristic
3	#15691794	C₄	1	4	yes	direct product factor
4	C₂×Dic₃₉₇	C₄	1	1	yes	characteristic
5	C₂×Dic₃₉₇	C₂²	1	1	yes	characteristic
6	C₂×C₄×C₃₉₇	C₄	1	1	yes	characteristic
7	C₂²×C₃₉₇	C₂×C₄	1	1	yes	characteristic
8	C₄×C₃₉₇	C₈	1	2	yes	complemented
9	Dic₃₉₇	C₈	1	2	yes	complemented
10	Dic₃₉₇	C₂×C₄	1	2	yes	—
11	C₂×C₃₉₇	C₄²	1	1	yes	characteristic
12	C₂×C₃₉₇	C₂×C₈	1	1	yes	characteristic
13	C₂×C₃₉₇	C₂×C₈	1	1	yes	characteristic
14	C₃₉₇	C₄×C₈	1	1	yes	characteristic, complemented, Sylow
15	C₄×C₈	—	397	1	no	maximal, Sylow
16	C₂×C₈	—	397	2	no	—
17	C₄²	—	397	1	no	—
18	C₂×C₄	—	397	1	no	—
19	C₂×C₄	—	397	1	no	—
20	C₂×C₄	#13097544	1	1	yes	characteristic
21	C₈	—	397	4	no	—
22	C₂²	C₂×#13097544	1	1	yes	characteristic
23	C₄	—	397	2	no	—
24	C₄	—	397	2	no	—
25	C₄	#15691794	1	2	yes	direct product factor
26	C₂	C₄×#13097544	1	1	yes	characteristic
27	C₂	C₂×#15691794	1	1	yes	characteristic
28	C₂	D₃₉₇⋊C₈	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.