Subgroups — C₂×#20263721 #27163113

Order 12704.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₇₉₄	C₂	1	1	yes	maximal, characteristic
2	#20263721	C₂	1	4	yes	maximal, direct product factor
3	C₂×#15691787	C₂	1	1	yes	maximal, characteristic
4	C₂×Q₈×C₃₉₇	C₂	1	1	yes	maximal, characteristic
5	Dic₇₉₄	—	2	1	no	—
6	Dic₇₉₄	C₂²	1	2	yes	—
7	C₂×Dic₃₉₇	—	2	1	no	—
8	#15691787	C₂²	1	2	yes	—
9	Q₈×C₃₉₇	—	2	1	no	—
10	Q₈×C₃₉₇	C₂²	1	2	yes	—
11	C₂×C₄×C₃₉₇	—	2	1	no	—
12	C₂×C₄×C₃₉₇	C₂²	1	1	yes	characteristic
13	C₂²×C₃₉₇	D₄	1	1	yes	characteristic
14	C₄×C₃₉₇	—	2	2	no	—
15	C₄×C₃₉₇	D₄	1	1	yes	characteristic
16	C₄×C₃₉₇	C₂³	1	1	yes	characteristic
17	Dic₃₉₇	—	2	2	no	—
18	C₂×C₃₉₇	Q₁₆	1	2	yes	complemented
19	C₂×C₃₉₇	C₂×D₄	1	1	yes	characteristic
20	C₃₉₇	C₂×Q₁₆	1	1	yes	characteristic, complemented, Sylow
21	C₂×Q₁₆	—	397	1	no	maximal, Sylow
22	C₂×Q₈	—	397	1	no	—
23	C₂×Q₈	D₃₉₇	1	1	yes	characteristic
24	Q₁₆	—	397	4	no	—
25	C₂×C₈	—	397	1	no	—
26	Q₈	—	2	1	no	—
27	Q₈	—	794	1	no	—
28	Q₈	—	397	2	no	—
29	Q₈	C₂×D₃₉₇	1	2	yes	—
30	C₂×C₄	—	2	1	no	—
31	C₂×C₄	—	794	1	no	—
32	C₂×C₄	C₂×D₃₉₇	1	1	yes	characteristic
33	C₈	—	397	2	no	—
34	C₂²	C₂²⋊D₃₉₇	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	794	2	no	—
37	C₄	C₂²⋊D₃₉₇	1	1	yes	characteristic
38	C₄	C₂²×D₃₉₇	1	1	yes	characteristic
39	C₂	#20263721	1	2	yes	direct product factor
40	C₂	C₂×C₂²⋊D₃₉₇	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.