Subgroups — #42122920

Order 27712.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#28357310	C₂	1	2	yes	maximal, complemented
2	#28357293	C₂	1	1	yes	maximal, characteristic
3	#20294100	C₄	1	1	yes	characteristic
4	#20294100	C₂²	1	1	yes	characteristic
5	C₈×D₄₃₃	C₄	1	1	yes	characteristic
6	C₄×D₄₃₃	C₈	1	1	yes	characteristic
7	#16812358	C₂×C₄	1	1	yes	characteristic
8	C₈×C₄₃₃	C₈	1	1	yes	characteristic
9	C₂×D₄₃₃	C₁₆	1	1	yes	characteristic
10	C₄×C₄₃₃	C₂×C₈	1	1	yes	characteristic
11	Dic₄₃₃	C₁₆	1	1	yes	characteristic
12	C₂×C₄₃₃	C₂×C₁₆	1	1	yes	characteristic
13	D₄₃₃	—	2	1	no	—
14	C₄₃₃	M₆₄	1	1	yes	characteristic, complemented, Sylow
15	M₆₄	—	433	1	no	maximal, Sylow
16	C₂×C₁₆	—	433	1	no	—
17	C₃₂	—	433	2	no	—
18	C₂×C₈	—	433	1	no	—
19	C₁₆	—	433	1	no	—
20	C₁₆	—	433	1	no	—
21	C₂×C₄	—	433	1	no	—
22	C₈	—	433	1	no	—
23	C₈	#16812367	1	1	yes	characteristic
24	C₂²	—	433	1	no	—
25	C₄	—	433	1	no	—
26	C₄	C₂×#16812367	1	1	yes	characteristic
27	C₂	—	866	1	no	—
28	C₂	#28357315	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #28357310	C₂	semidirect
14. C₄₃₃	M₆₄	semidirect

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