Subgroups — C₃×C₃⋊#13063703 #27160271

Order 12564.

28 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×D₃₄₉	C₂	1	1	yes	maximal, characteristic
2	C₃⋊#13063703	C₃	1	1	yes	maximal, characteristic, direct product factor
3	C₃×#13063703	—	3	1	no	maximal
4	C₃²×C₃₄₉	C₄	1	1	yes	characteristic, complemented, Hall
5	C₃×D₃₄₉	—	2	1	no	—
6	C₃×D₃₄₉	D₃	1	1	yes	characteristic
7	C₃×D₃₄₉	C₂×C₃	1	1	yes	characteristic
8	#13063703	—	3	1	no	Hall
9	C₃×C₃₄₉	—	2	1	no	—
10	C₃×C₃₄₉	Dic₃	1	1	yes	characteristic, complemented
11	C₃×C₃₄₉	C₃×C₄	1	1	yes	characteristic, complemented
12	D₃₄₉	C₃×D₃	1	1	yes	characteristic
13	C₃₄₉	C₃×Dic₃	1	1	yes	characteristic, complemented, Sylow
14	C₃×Dic₃	—	349	1	no	maximal, Hall
15	C₂×C₃²	—	349	1	no	—
16	C₃×C₄	—	1047	1	no	—
17	Dic₃	—	349	1	no	—
18	C₃²	#13063703	1	1	yes	characteristic, complemented, Sylow
19	C₂×C₃	—	349	1	no	—
20	C₂×C₃	—	349	1	no	—
21	C₂×C₃	—	698	1	no	—
22	C₄	—	1047	1	no	Sylow
23	C₃	—	2	1	no	—
24	C₃	C₃×#13063703	1	1	yes	characteristic, complemented
25	C₃	C₃⋊#13063703	1	1	yes	characteristic, direct product factor
26	C₂	—	349	1	no	—

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.