Subgroups — #30634010

Order 16227.

16 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₆₀₁⋊C₃	C₃	1	1	yes	maximal, characteristic
2	C₉×C₆₀₁	C₃	1	1	yes	maximal, characteristic, complemented
3	C₆₀₁⋊C₉	C₃	1	2	yes	maximal, complemented
4	C₃×C₆₀₁	C₃²	1	1	yes	characteristic
5	C₆₀₁⋊C₃	—	3	1	no	—
6	C₆₀₁	3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
7	3₋¹⁺²	—	601	1	no	maximal, Sylow
8	C₃²	—	601	1	no	—
9	C₉	—	601	2	no	—
10	C₉	C₆₀₁⋊C₃	1	1	yes	characteristic, complemented
11	C₃	—	1803	1	no	—
12	C₃	C₃×C₆₀₁⋊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.