Subgroups — #1144⋊C₃ #66552

Order 336.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×ΓL(1,𝔽₈)	C₂	1	1	yes	maximal, characteristic
2	ΓL(1,𝔽₈)⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	ΓL(1,𝔽₈)⋊C₈	C₂	1	1	yes	maximal, characteristic
4	#1144	C₃	1	1	yes	maximal, characteristic, complemented, Hall
5	C₄×ΓL(1,𝔽₈)	—	2	1	no	—
6	C₄×ΓL(1,𝔽₈)	C₂²	1	1	yes	characteristic
7	ΓL(1,𝔽₈)⋊C₄	—	2	1	no	—
8	C₇×Q₈	C₂×C₃	1	1	yes	characteristic
9	Dic₁₄	C₂×C₃	1	1	yes	characteristic
10	C₇⋊C₈	C₂×C₃	1	1	yes	characteristic
11	C₃×Q₁₆	—	7	1	no	maximal, Hall
12	C₂×ΓL(1,𝔽₈)	D₄	1	1	yes	characteristic
13	C₄×C₇	—	2	1	no	—
14	C₄×C₇	C₂²×C₃	1	1	yes	characteristic
15	Dic₇	—	2	1	no	—
16	C₃×Q₈	—	7	1	no	—
17	C₃×Q₈	—	7	1	no	—
18	C₃×C₈	—	7	1	no	—
19	ΓL(1,𝔽₈)	Q₁₆	1	1	yes	characteristic, complemented, Hall
20	Q₁₆	—	7	1	no	Sylow
21	C₂×C₇	C₃×D₄	1	1	yes	characteristic
22	C₃×C₄	—	7	1	no	—
23	C₃×C₄	—	14	1	no	—
24	C₃×C₄	—	14	1	no	—
25	Q₈	—	7	1	no	—
26	Q₈	AGL(1,𝔽₇)	1	1	yes	characteristic
27	C₈	—	7	1	no	—
28	C₇	C₃×Q₁₆	1	1	yes	characteristic, complemented, Sylow
29	C₂×C₃	—	7	1	no	—
30	C₄	—	2	1	no	—
31	C₄	—	14	1	no	—
32	C₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic
33	C₃	—	7	1	no	Sylow
34	C₂	(C₂²⋊D₇)⋊C₃	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.