Subgroups — #45688324

Order 33344.

46 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30659782	C₂	1	2	yes	maximal
2	#30659619	C₂	1	1	yes	maximal, characteristic
3	#22552367	C₄	1	4	yes	complemented
4	C₂×#16861960	C₄	1	1	yes	characteristic
5	C₂×#16861960	C₂²	1	1	yes	characteristic
6	C₄²×C₅₂₁	C₄	1	1	yes	characteristic
7	#16861960	—	2	1	no	—
8	#16861960	C₂×C₄	1	2	yes	—
9	C₂×C₄×C₅₂₁	—	2	1	no	—
10	C₂×C₄×C₅₂₁	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₅₂₁	M₁₆	1	1	yes	characteristic
12	C₄×C₅₂₁	—	4	1	no	—
13	C₄×C₅₂₁	C₄²	1	1	yes	characteristic
14	C₄×C₅₂₁	M₁₆	1	1	yes	characteristic
15	C₂×C₅₂₁	—	2	1	no	—
16	C₂×C₅₂₁	#97	1	1	yes	characteristic
17	C₅₂₁	#347	1	1	yes	characteristic, complemented, Sylow
18	#347	—	521	1	no	maximal, Sylow
19	M₃₂	—	521	2	no	—
20	#97	—	521	1	no	—
21	C₂×C₈	—	521	1	no	—
22	C₂×C₈	—	521	1	no	—
23	C₄²	#14523438	1	1	yes	characteristic
24	C₁₆	—	521	4	no	—
25	C₂×C₄	—	2	1	no	—
26	C₂×C₄	C₂×#14523438	1	1	yes	characteristic
27	C₈	—	521	2	no	—
28	C₈	—	1042	1	no	—
29	C₂²	#22552373	1	1	yes	characteristic
30	C₄	—	4	1	no	—
31	C₄	C₄×#14523438	1	1	yes	characteristic
32	C₄	#22552374	1	1	yes	characteristic
33	C₂	—	2	1	no	—
34	C₂	#30659763	1	1	yes	characteristic

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

N	H ≅ G/N	type
3. #22552367	C₄	semidirect
17. C₅₂₁	#347	semidirect

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