Subgroups — #17987584

Order 4617.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13095335	C₃	1	3	yes	maximal, complemented
2	C₂₇×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₉×C₁₉⋊C₃	C₉	1	1	yes	characteristic
4	C₁₉×C₂₇	C₉	1	1	yes	characteristic
5	#10587018	C₉	1	1	yes	characteristic
6	#10587018	C₃²	1	1	yes	characteristic
7	C₈₁⋊C₃	—	19	1	no	maximal, Sylow
8	C₃×C₁₉⋊C₃	C₂₇	1	1	yes	characteristic
9	C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
10	#4294	C₂₇	1	2	yes	—
11	C₃×C₂₇	—	19	1	no	—
12	C₈₁	—	19	3	no	—
13	C₃×C₁₉	C₃×C₂₇	1	1	yes	characteristic
14	C₁₉⋊C₃	—	3	1	no	—
15	C₃×C₉	—	19	1	no	—
16	C₂₇	—	19	1	no	—
17	C₂₇	—	19	1	no	—
18	C₂₇	#4296	1	1	yes	characteristic
19	C₁₉	C₈₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
20	C₃²	—	19	1	no	—
21	C₉	—	19	2	no	—
22	C₉	C₃×#4296	1	1	yes	characteristic
23	C₃	—	57	1	no	—
24	C₃	(C₁₉⋊C₃)⋊C₂₇	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #13095335	C₃	semidirect
19. C₁₉	C₈₁⋊C₃	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.