Subgroups — #27163164

Order 12704.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#13097544	C₂	1	2	yes	maximal
2	C₈×D₃₉₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#13097544	—	2	2	no	—
4	C₄×D₃₉₇	C₂²	1	1	yes	characteristic
5	#15691787	C₄	1	1	yes	characteristic, complemented
6	C₈×C₃₉₇	C₄	1	1	yes	characteristic, complemented
7	C₂×D₃₉₇	D₄	1	1	yes	characteristic
8	#13097544	—	4	2	no	—
9	C₄×C₃₉₇	C₂×C₄	1	1	yes	characteristic
10	Dic₃₉₇	Q₈	1	1	yes	characteristic
11	C₂×C₃₉₇	C₄⋊C₄	1	1	yes	characteristic
12	D₃₉₇	SD₁₆	1	2	yes	—
13	C₃₉₇	#106	1	1	yes	characteristic, complemented, Sylow
14	#106	—	397	1	no	maximal, Sylow
15	C₂×C₈	—	397	1	no	—
16	C₄⋊C₄	—	397	2	no	—
17	C₂×C₄	—	794	2	no	—
18	C₂×C₄	—	397	1	no	—
19	C₈	—	397	1	no	—
20	C₈	#13097544	1	1	yes	characteristic, complemented
21	C₂²	—	397	1	no	—
22	C₄	—	1588	2	no	—
23	C₄	—	397	1	no	—
24	C₄	C₂×#13097544	1	1	yes	characteristic
25	C₂	—	397	2	no	—
26	C₂	C₄⋊#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.