Subgroups — #28357290

Order 13856.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20294107	C₂	1	2	yes	maximal
2	C₈×D₄₃₃	C₂	1	1	yes	maximal, characteristic
3	#16812365	—	2	2	no	—
4	C₄×D₄₃₃	C₂²	1	1	yes	characteristic
5	#16812358	C₄	1	1	yes	characteristic
6	C₈×C₄₃₃	C₄	1	1	yes	characteristic
7	C₂×D₄₃₃	Q₈	1	1	yes	characteristic
8	C₄×C₄₃₃	C₂×C₄	1	1	yes	characteristic
9	Dic₄₃₃	D₄	1	1	yes	characteristic
10	C₂×C₄₃₃	C₄⋊C₄	1	1	yes	characteristic
11	D₄₃₃	—	2	1	no	—
12	C₄₃₃	#108	1	1	yes	characteristic, complemented, Sylow
13	#108	—	433	1	no	maximal, Sylow
14	M₁₆	—	433	2	no	—
15	C₂×C₈	—	433	1	no	—
16	C₂×C₄	—	433	1	no	—
17	C₈	—	866	2	no	—
18	C₈	—	433	1	no	—
19	C₈	#13181884	1	1	yes	characteristic
20	C₂²	—	433	1	no	—
21	C₄	—	433	1	no	—
22	C₄	C₂×#13181884	1	1	yes	characteristic
23	C₂	—	866	1	no	—
24	C₂	C₄⋊#13181884	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. C₄₃₃	#108	semidirect

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