Subgroups — 3₋¹⁺²×C₃₇₉⋊C₃ #44501950

Order 30699.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₇₉⋊C₃	C₃	1	1	yes	maximal, characteristic
2	#23779522	C₃	1	2	yes	maximal, complemented
3	#23779521	C₃	1	3	yes	maximal, complemented
4	#23779520	C₃	1	3	yes	maximal, complemented
5	C₉×C₃₇₉⋊C₃	C₃	1	3	yes	maximal, complemented
6	3₋¹⁺²×C₃₇₉	C₃	1	1	yes	maximal, characteristic, complemented
7	C₃²×C₃₇₉	C₃²	1	1	yes	characteristic
8	C₃×C₃₇₉⋊C₃	—	3	3	no	—
9	C₃×C₃₇₉⋊C₃	C₃²	1	1	yes	characteristic
10	C₃×C₃₇₉⋊C₃	C₃²	1	1	yes	characteristic
11	C₃×C₃₇₉⋊C₃	C₃²	1	1	yes	characteristic
12	C₉×C₃₇₉	C₃²	1	3	yes	complemented
13	#16811787	C₃²	1	6	yes	complemented
14	C₃×C₃₇₉	—	3	1	no	—
15	C₃×C₃₇₉	C₃³	1	1	yes	characteristic
16	C₃₇₉⋊C₃	—	3	1	no	—
17	C₃₇₉⋊C₃	—	3	1	no	—
18	C₃₇₉⋊C₃	3₋¹⁺²	1	3	yes	direct product factor
19	C₃₇₉	C₃×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
20	C₃×3₋¹⁺²	—	379	1	no	maximal, Sylow
21	C₃³	—	379	1	no	—
22	3₋¹⁺²	—	379	2	no	—
23	3₋¹⁺²	—	379	3	no	—
24	3₋¹⁺²	—	379	3	no	—
25	3₋¹⁺²	C₃₇₉⋊C₃	1	1	yes	characteristic, direct product factor
26	C₃×C₉	—	379	3	no	—
27	C₃²	—	1137	3	no	—
28	C₃²	—	379	1	no	—
29	C₃²	—	379	1	no	—
30	C₃²	—	379	1	no	—
31	C₃²	C₃×C₃₇₉⋊C₃	1	1	yes	characteristic
32	C₉	—	379	6	no	—
33	C₉	C₃×C₃₇₉⋊C₃	1	3	yes	complemented
34	C₃	—	3	1	no	—
35	C₃	—	1137	1	no	—
36	C₃	—	1137	1	no	—
37	C₃	—	379	3	no	—
38	C₃	C₃²×C₃₇₉⋊C₃	1	1	yes	characteristic

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.