Subgroups — C₃×#20264238 #34063233

Order 19197.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₇₉⋊C₉	C₃	1	3	yes	maximal
2	#20264238	C₃	1	9	yes	maximal, direct product factor
3	C₃²×C₉×C₇₉	C₃	1	1	yes	maximal, characteristic
4	C₃×C₇₉⋊C₉	—	3	9	no	—
5	C₃×C₇₉⋊C₉	C₃²	1	9	yes	—
6	C₃³×C₇₉	C₃²	1	1	yes	characteristic
7	C₃×C₉×C₇₉	C₉	1	9	yes	complemented
8	C₃×C₉×C₇₉	C₃²	1	3	yes	—
9	C₃²×C₇₉	C₃×C₉	1	3	yes	—
10	C₃²×C₇₉	3₋¹⁺²	1	9	yes	—
11	C₃²×C₇₉	C₃³	1	1	yes	characteristic
12	C₉×C₇₉	C₃×C₉	1	9	yes	complemented
13	C₇₉⋊C₉	—	3	9	no	—
14	C₃×C₉⋊C₉	—	79	1	no	maximal, Sylow
15	C₃×C₇₉	C₉⋊C₉	1	9	yes	complemented
16	C₃×C₇₉	C₃²×C₉	1	1	yes	characteristic
17	C₃×C₇₉	C₃×3₋¹⁺²	1	3	yes	—
18	C₃²×C₉	—	79	3	no	—
19	C₃²×C₉	C₇₉⋊C₃	1	1	yes	characteristic
20	C₉⋊C₉	—	79	9	no	—
21	C₇₉	C₃×C₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
22	C₃³	C₃×C₇₉⋊C₃	1	1	yes	characteristic
23	C₃×C₉	—	79	9	no	—
24	C₃×C₉	—	237	9	no	—
25	C₃×C₉	C₇₉⋊C₉	1	9	yes	complemented
26	C₃×C₉	C₃×C₇₉⋊C₃	1	3	yes	—
27	C₃²	C₃×C₇₉⋊C₉	1	3	yes	—
28	C₃²	#14523838	1	9	yes	—
29	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
30	C₉	—	237	9	no	—
31	C₉	C₃×C₇₉⋊C₉	1	9	yes	complemented
32	C₃	#20264238	1	9	yes	direct product factor
33	C₃	C₃²×C₇₉⋊C₉	1	1	yes	characteristic
34	C₃	C₃×#14523838	1	3	yes	—

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.