Subgroups — #66561

Order 336.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₂₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	D₅₆	—	3	1	no	maximal, Hall
5	C₂×D₂₁	—	2	1	no	—
6	C₂×C₃×D₇	—	2	1	no	—
7	C₃×C₄×C₇	C₂²	1	1	yes	characteristic
8	D₂₈	—	3	1	no	—
9	D₂₈	D₃	1	1	yes	characteristic, complemented
10	C₇×C₈	—	3	1	no	—
11	#213	—	7	1	no	maximal, Hall
12	C₂×C₃×C₇	D₄	1	1	yes	characteristic
13	D₂₁	—	4	1	no	—
14	C₃×D₇	—	4	1	no	—
15	C₂×D₇	—	2	1	no	—
16	C₂×D₇	—	6	1	no	—
17	C₄×C₇	C₂×D₃	1	1	yes	characteristic
18	C₃×D₄	—	7	1	no	—
19	D₁₂	—	7	1	no	—
20	C₃⋊C₈	D₇	1	1	yes	characteristic, complemented
21	C₃×C₇	D₈	1	1	yes	characteristic, complemented, Hall
22	D₈	—	21	1	no	Sylow
23	C₂×C₇	#67	1	1	yes	characteristic
24	D₇	—	4	1	no	—
25	D₇	—	12	1	no	—
26	C₂²×C₃	—	14	1	no	—
27	C₂×D₃	—	14	1	no	—
28	C₃×C₄	C₂×D₇	1	1	yes	characteristic
29	D₄	—	7	1	no	—
30	D₄	—	21	1	no	—
31	C₈	—	3	1	no	—
32	C₇	#213	1	1	yes	characteristic, complemented, Sylow
33	C₂×C₃	—	28	1	no	—
34	C₂×C₃	D₂₈	1	1	yes	characteristic
35	D₃	—	28	1	no	—
36	C₂²	—	14	1	no	—
37	C₂²	—	42	1	no	—
38	C₄	D₃×D₇	1	1	yes	characteristic
39	C₃	D₅₆	1	1	yes	characteristic, complemented, Sylow
40	C₂	—	28	1	no	—
41	C₂	—	84	1	no	—
42	C₂	#4246	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.