Subgroups — #27163155

Order 12704.

52 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#13097544	C₂	1	2	yes	maximal, complemented
2	C₂×D₁₅₈₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#13097544	—	2	2	no	—
4	C₂²×D₃₉₇	C₄	1	1	yes	characteristic, complemented
5	C₂²×D₃₉₇	C₂²	1	1	yes	characteristic
6	D₁₅₈₈	—	2	2	no	—
7	C₂×C₄×C₃₉₇	C₄	1	1	yes	characteristic, complemented
8	C₂²×C₃₉₇	C₂×C₄	1	1	yes	characteristic
9	C₂×D₃₉₇	—	2	1	no	—
10	C₂×D₃₉₇	—	4	1	no	—
11	C₂×D₃₉₇	—	4	1	no	—
12	C₂×D₃₉₇	D₄	1	2	yes	—
13	#13097544	—	4	2	no	—
14	C₄×C₃₉₇	—	2	1	no	—
15	C₂×C₃₉₇	—	2	1	no	—
16	C₂×C₃₉₇	C₂²⋊C₄	1	1	yes	characteristic
17	D₃₉₇	—	2	2	no	—
18	D₃₉₇	—	4	1	no	—
19	C₃₉₇	#99	1	1	yes	characteristic, complemented, Sylow
20	#99	—	397	1	no	maximal, Sylow
21	C₂×D₄	—	397	1	no	—
22	C₂²⋊C₄	—	397	2	no	—
23	C₂³	—	397	1	no	—
24	C₂³	—	397	1	no	—
25	D₄	—	794	2	no	—
26	C₂×C₄	—	794	2	no	—
27	C₂×C₄	#13097544	1	1	yes	characteristic, complemented
28	C₂²	—	794	1	no	—
29	C₂²	—	1588	1	no	—
30	C₂²	—	1588	1	no	—
31	C₂²	—	397	2	no	—
32	C₂²	C₂×#13097544	1	1	yes	characteristic
33	C₄	—	2	1	no	—
34	C₄	—	1588	2	no	—
35	C₂	—	2	1	no	—
36	C₂	—	794	2	no	—
37	C₂	—	1588	1	no	—
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.