Subgroups — C₄⋊#15691794 #27163162

Order 12704.

38 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	—	2	2	no	—
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	—	2	1	no	—
10	Dic₃₉₇	D₄	1	1	yes	characteristic
11	Dic₃₉₇	Q₈	1	1	yes	characteristic
12	C₂×C₃₉₇	C₄⋊C₄	1	1	yes	characteristic
13	C₂×C₃₉₇	C₂×C₈	1	1	yes	characteristic
14	C₂×C₃₉₇	M₁₆	1	1	yes	characteristic
15	C₃₉₇	C₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
16	C₄⋊C₈	—	397	1	no	maximal, Sylow
17	C₂×C₈	—	397	2	no	—
18	C₄²	—	397	1	no	—
19	C₂×C₄	—	397	1	no	—
20	C₂×C₄	—	397	1	no	—
21	C₂×C₄	#13097544	1	1	yes	characteristic
22	C₈	—	794	2	no	—
23	C₂²	C₂×#13097544	1	1	yes	characteristic
24	C₄	—	794	1	no	—
25	C₄	—	397	1	no	—
26	C₄	—	397	1	no	—
27	C₄	#15691794	1	2	yes	complemented
28	C₂	C₄⋊#13097544	1	1	yes	characteristic
29	C₂	C₂×#15691794	1	1	yes	characteristic
30	C₂	#20263741	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.