Subgroups — #66634

Order 336.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	D₈₄	C₂	1	1	yes	maximal, characteristic
3	C₃⋊(C₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
4	#1143	—	3	1	no	maximal, Hall
5	C₂×D₂₁	—	2	1	no	—
6	C₃×C₄×C₇	—	2	1	no	—
7	C₃×C₄×C₇	C₂²	1	1	yes	characteristic
8	C₇×Q₈	D₃	1	1	yes	characteristic, complemented
9	D₂₈	—	3	1	no	—
10	C₇⋊C₈	—	3	1	no	—
11	#215	—	7	1	no	maximal, Hall
12	C₂×C₃×C₇	D₄	1	1	yes	characteristic
13	D₂₁	—	4	1	no	—
14	C₂×D₇	—	6	1	no	—
15	C₄×C₇	—	2	1	no	—
16	C₄×C₇	C₂×D₃	1	1	yes	characteristic
17	C₃×Q₈	D₇	1	1	yes	characteristic, complemented
18	D₁₂	—	7	1	no	—
19	C₃⋊C₈	—	7	1	no	—
20	C₃×C₇	SD₁₆	1	1	yes	characteristic, complemented, Hall
21	SD₁₆	—	21	1	no	Sylow
22	C₂×C₇	#67	1	1	yes	characteristic
23	D₇	—	12	1	no	—
24	C₂×D₃	—	14	1	no	—
25	C₃×C₄	—	2	1	no	—
26	C₃×C₄	C₂×D₇	1	1	yes	characteristic
27	Q₈	D₂₁	1	1	yes	characteristic, complemented
28	D₄	—	21	1	no	—
29	C₈	—	21	1	no	—
30	C₇	#215	1	1	yes	characteristic, complemented, Sylow
31	C₂×C₃	C₂²⋊D₇	1	1	yes	characteristic
32	D₃	—	28	1	no	—
33	C₂²	—	42	1	no	—
34	C₄	—	2	1	no	—
35	C₄	C₂×D₂₁	1	1	yes	characteristic
36	C₃	#1143	1	1	yes	characteristic, complemented, Sylow
37	C₂	—	84	1	no	—
38	C₂	#4268	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.