Subgroups — #34063301

Order 19197.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14523839	C₃	1	4	yes	maximal
2	#20264237	C₃	1	8	yes	maximal, complemented
3	C₉²×C₇₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₇₉⋊C₃	C₃²	1	1	yes	characteristic
5	#14523839	—	3	12	no	—
6	C₃×C₇₉⋊C₉	C₃²	1	8	yes	—
7	C₃×C₉×C₇₉	C₃²	1	4	yes	—
8	C₃²×C₇₉	C₃³	1	1	yes	characteristic
9	C₃×C₇₉⋊C₃	—	3	4	no	—
10	C₉×C₇₉	3₋¹⁺²	1	12	yes	complemented
11	C₇₉⋊C₉	—	3	8	no	—
12	#6900	—	79	1	no	maximal, Sylow
13	C₃×C₇₉	C₃×3₋¹⁺²	1	4	yes	—
14	C₇₉⋊C₃	—	9	1	no	—
15	C₃×3₋¹⁺²	—	79	4	no	—
16	C₉⋊C₉	—	79	8	no	—
17	C₉²	C₇₉⋊C₃	1	1	yes	characteristic, complemented
18	C₇₉	#6900	1	1	yes	characteristic, complemented, Sylow
19	C₃³	—	79	1	no	—
20	3₋¹⁺²	—	237	12	no	—
21	C₃×C₉	—	79	8	no	—
22	C₃×C₉	C₃×C₇₉⋊C₃	1	4	yes	—
23	C₃²	—	237	4	no	—
24	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
25	C₉	—	237	8	no	—
26	C₉	#14523839	1	12	yes	complemented
27	C₃	—	711	1	no	—
28	C₃	C₃×#14523839	1	4	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.