Subgroups — C₂×#1136 #6484

Order 224.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₇	C₂	1	1	yes	maximal, characteristic
2	#1136	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₇⋊C₈	C₂	1	2	yes	maximal, complemented
4	C₂³×C₇	C₄	1	1	yes	characteristic
5	C₂×C₄×C₇	C₄	1	2	yes	—
6	C₂×C₄×C₇	C₄	1	1	yes	characteristic
7	C₂×C₄×C₇	C₂²	1	2	yes	—
8	C₂×C₄×C₇	C₂²	1	1	yes	characteristic
9	C₇⋊C₈	C₂²	1	4	yes	complemented
10	C₂×M₁₆	—	7	1	no	maximal, Sylow
11	C₂²×C₇	—	2	2	no	—
12	C₂²×C₇	C₂×C₄	1	2	yes	—
13	C₂²×C₇	C₂×C₄	1	1	yes	characteristic
14	C₄×C₇	C₂×C₄	1	2	yes	—
15	C₄×C₇	C₂×C₄	1	1	yes	characteristic
16	C₄×C₇	C₂³	1	1	yes	characteristic
17	C₂²×C₄	D₇	1	1	yes	characteristic
18	M₁₆	—	7	4	no	—
19	C₂×C₈	—	7	2	no	—
20	C₂×C₇	—	2	2	no	—
21	C₂×C₇	M₁₆	1	2	yes	complemented
22	C₂×C₇	C₂²×C₄	1	1	yes	characteristic
23	C₂³	Dic₇	1	1	yes	characteristic
24	C₂×C₄	Dic₇	1	1	yes	characteristic
25	C₂×C₄	Dic₇	1	2	yes	—
26	C₂×C₄	C₂×D₇	1	2	yes	—
27	C₂×C₄	C₂×D₇	1	1	yes	characteristic
28	C₈	—	7	4	no	—
29	C₇	C₂×M₁₆	1	1	yes	characteristic, complemented, Sylow
30	C₂²	—	2	2	no	—
31	C₂²	C₂×Dic₇	1	2	yes	—
32	C₂²	C₂×Dic₇	1	1	yes	characteristic
33	C₄	C₂×Dic₇	1	2	yes	—
34	C₄	C₂×Dic₇	1	1	yes	characteristic
35	C₄	C₂²×D₇	1	1	yes	characteristic
36	C₂	—	2	2	no	—
37	C₂	#1136	1	2	yes	direct product factor
38	C₂	C₂²×Dic₇	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.