Subgroups — #44446209

Order 29727.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₆₇⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
2	#23755308	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²⋊(C₃₆₇⋊C₃)	C₃	1	1	yes	maximal, characteristic, complemented
4	3₋¹⁺²×C₃₆₇	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃²×C₃₆₇	C₃²	1	1	yes	characteristic
6	C₃×C₃₆₇⋊C₃	—	3	1	no	—
7	C₃×C₃₆₇⋊C₃	—	3	3	no	—
8	C₃×C₃₆₇⋊C₃	—	3	1	no	—
9	C₉×C₃₆₇	—	3	1	no	—
10	C₃₆₇⋊C₉	—	3	1	no	—
11	C₃×C₃₆₇	—	3	1	no	—
12	C₃×C₃₆₇	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃₆₇⋊C₃	—	3	3	no	—
14	C₃₆₇⋊C₃	—	9	1	no	—
15	C₃₆₇	AΣL(1,𝔽₂₇)	1	1	yes	characteristic, complemented, Sylow
16	AΣL(1,𝔽₂₇)	—	367	1	no	maximal, Sylow
17	C₃³	—	367	1	no	—
18	3₋¹⁺²	—	367	1	no	—
19	3₋¹⁺²	C₃₆₇⋊C₃	1	1	yes	characteristic, complemented
20	H(3,𝔽₃)	—	367	1	no	—
21	C₃²	—	1101	3	no	—
22	C₃²	—	1101	1	no	—
23	C₃²	—	1101	1	no	—
24	C₃²	C₃×C₃₆₇⋊C₃	1	1	yes	characteristic
25	C₉	—	3	1	no	—
26	C₉	—	1101	1	no	—
27	C₃	—	3	1	no	—
28	C₃	—	1101	3	no	—
29	C₃	—	3303	1	no	—
30	C₃	C₃²⋊(C₃₆₇⋊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.