Subgroups — (C₃⋊D₃)⋊D₂₉₃ #24902147

Order 10548.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₂₉₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×D₈₇₉	C₂	1	2	yes	maximal, complemented
3	D₃×D₂₉₃	—	3	2	no	maximal
4	C₃²×C₂₉₃	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₈₇₉	D₃	1	2	yes	complemented
6	C₃×D₂₉₃	—	3	2	no	—
7	D₃×C₂₉₃	—	3	2	no	—
8	D₃×C₂₉₃	—	6	1	no	—
9	C₂×D₂₉₃	—	9	1	no	Hall
10	C₃×C₂₉₃	—	2	1	no	—
11	C₃×C₂₉₃	C₂×D₃	1	2	yes	complemented
12	C₂×C₂₉₃	—	9	1	no	—
13	D₂₉₃	—	3	2	no	—
14	C₂₉₃	D₃²	1	1	yes	characteristic, complemented, Sylow
15	D₃²	—	293	1	no	maximal, Hall
16	C₃⋊D₃	D₂₉₃	1	1	yes	characteristic, complemented
17	C₃×D₃	—	293	2	no	—
18	C₂×D₃	—	879	2	no	—
19	C₃²	C₂×D₂₉₃	1	1	yes	characteristic, complemented, Sylow
20	C₂×C₃	—	879	2	no	—
21	D₃	—	3	2	no	—
22	D₃	—	6	1	no	—
23	D₃	—	293	2	no	—
24	C₂²	—	2637	1	no	Sylow
25	C₃	—	2	1	no	—
26	C₃	D₃×D₂₉₃	1	2	yes	complemented
27	C₂	—	9	1	no	—
28	C₂	—	879	2	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃²×C₂₉₃	C₂²
LCS	G ▷ C₃²×C₂₉₃
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.