Subgroups — C₂⁶×D₃ #87592

Order 384.

58424 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂⁵×D₃	C₂	1	126	yes	maximal, direct product factor
3	C₂⁷	—	3	1	no	maximal, Sylow
4	C₂⁵×C₃	C₂²	1	63	yes	complemented
5	C₂⁴×D₃	C₂²	1	2604	yes	direct product factor
6	C₂⁶	—	3	126	no	—
7	C₂⁶	D₃	1	1	yes	characteristic, direct product factor
8	C₂⁴×C₃	C₂³	1	651	yes	complemented
9	C₂³×D₃	C₂³	1	11160	yes	direct product factor
10	C₂⁵	—	3	2604	no	—
11	C₂⁵	C₂×D₃	1	63	yes	direct product factor
12	C₂³×C₃	C₂⁴	1	1395	yes	complemented
13	C₂²×D₃	C₂⁴	1	10416	yes	direct product factor
14	C₂⁴	—	3	11160	no	—
15	C₂⁴	C₂²×D₃	1	651	yes	direct product factor
16	C₂²×C₃	C₂⁵	1	651	yes	complemented
17	C₂×D₃	C₂⁵	1	2016	yes	direct product factor
18	C₂³	—	3	10416	no	—
19	C₂³	C₂³×D₃	1	1395	yes	direct product factor
20	C₂×C₃	C₂⁶	1	63	yes	complemented
21	D₃	C₂⁶	1	64	yes	direct product factor
22	C₂²	—	3	2016	no	—
23	C₂²	C₂⁴×D₃	1	651	yes	direct product factor
24	C₃	C₂⁷	1	1	yes	characteristic, complemented, Sylow
25	C₂	—	3	64	no	—
26	C₂	C₂⁵×D₃	1	63	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁶	D₃
commutator, cosocle, hypocenter	C₃	C₂⁷
Frattini	C₁	G
Fitting, socle	C₂⁶×C₃	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂⁶

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.