Subgroups — #20301063

Order 7328.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16814669	C₂	1	2	yes	maximal, complemented
2	C₈×D₂₂₉	C₂	1	1	yes	maximal, characteristic
3	C₄×D₂₂₉	C₄	1	1	yes	characteristic
4	#14270080	C₂²	1	1	yes	characteristic
5	C₈×C₂₂₉	C₄	1	1	yes	characteristic
6	C₂×D₂₂₉	C₈	1	1	yes	characteristic
7	C₄×C₂₂₉	C₂×C₄	1	1	yes	characteristic
8	Dic₂₂₉	C₈	1	1	yes	characteristic
9	C₂×C₂₂₉	C₂×C₈	1	1	yes	characteristic
10	D₂₂₉	—	2	1	no	—
11	C₂₂₉	M₃₂	1	1	yes	characteristic, complemented, Sylow
12	M₃₂	—	229	1	no	maximal, Sylow
13	C₂×C₈	—	229	1	no	—
14	C₁₆	—	229	2	no	—
15	C₂×C₄	—	229	1	no	—
16	C₈	—	229	1	no	—
17	C₈	#11745021	1	1	yes	characteristic
18	C₂²	—	229	1	no	—
19	C₄	—	229	1	no	—
20	C₄	C₂×#11745021	1	1	yes	characteristic
21	C₂	—	458	1	no	—
22	C₂	D₂₂₉⋊C₈	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #16814669	C₂	semidirect
11. C₂₂₉	M₃₂	semidirect