Subgroups — #49154261

Order 37503.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²⋊(C₄₆₃⋊C₃)	C₃	1	3	yes	maximal, complemented
2	C₃×C₉×C₄₆₃	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²×C₄₆₃	C₃²	1	1	yes	characteristic
4	C₃×C₄₆₃⋊C₃	—	3	3	no	—
5	C₉×C₄₆₃	—	3	1	no	—
6	C₃×C₄₆₃	—	3	1	no	—
7	C₃×C₄₆₃	H(3,𝔽₃)	1	1	yes	characteristic
8	C₄₆₃⋊C₃	—	9	3	no	—
9	C₄₆₃	#732	1	1	yes	characteristic, complemented, Sylow
10	#732	—	463	1	no	maximal, Sylow
11	H(3,𝔽₃)	—	463	3	no	—
12	C₃×C₉	C₄₆₃⋊C₃	1	1	yes	characteristic, complemented
13	C₃²	—	1389	3	no	—
14	C₃²	C₃×C₄₆₃⋊C₃	1	1	yes	characteristic
15	C₉	—	3	1	no	—
16	C₃	—	3	1	no	—
17	C₃	—	4167	3	no	—
18	C₃	C₃²⋊(C₄₆₃⋊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.