Subgroups — C₇×C₂²⋊(C₂²⋊A₄) #13062426

Order 1344.

2030 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×C₇	C₃	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇×C₂²⋊A₄	—	4	21	no	maximal
3	C₂⁵×C₇	—	3	21	no	—
4	C₂²⋊(C₂²⋊A₄)	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
5	C₂⁴×C₇	—	3	210	no	—
6	C₂⁴×C₇	A₄	1	21	yes	complemented
7	C₇×A₄	—	16	21	no	—
8	C₂⁶	C₃×C₇	1	1	yes	characteristic, complemented, Sylow
9	C₂³×C₇	—	3	360	no	—
10	C₂³×C₇	—	3	105	no	—
11	C₂²⋊A₄	—	4	21	no	—
12	C₂⁵	—	3	21	no	—
13	C₂²×C₇	—	3	210	no	—
14	C₂²×C₇	C₂²⋊A₄	1	21	yes	complemented
15	C₃×C₇	—	64	1	no	Hall
16	C₂⁴	—	3	210	no	—
17	C₂⁴	C₇×A₄	1	21	yes	complemented
18	C₂×C₇	—	3	21	no	—
19	A₄	—	16	21	no	—
20	C₂³	—	3	360	no	—
21	C₂³	—	3	105	no	—
22	C₇	C₂²⋊(C₂²⋊A₄)	1	1	yes	characteristic, direct product factor, Sylow
23	C₂²	—	3	210	no	—
24	C₂²	C₇×C₂²⋊A₄	1	21	yes	complemented
25	C₃	—	64	1	no	Sylow
26	C₂	—	3	21	no	—

	subgroup	G/H
center, hypercenter	C₇	C₂²⋊(C₂²⋊A₄)
commutator, cosocle, hypocenter	C₂⁶	C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂⁶×C₇	C₃
LCS	G ▷ C₂⁶
UCS	C₁ ◁ C₇

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.