Subgroups — #22575523

Order 8608.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16864412	C₂	1	2	yes	maximal
2	C₈×D₂₆₉	C₂	1	1	yes	maximal, characteristic
3	#14524137	—	2	2	no	—
4	C₄×D₂₆₉	C₂²	1	1	yes	characteristic
5	#14524130	C₄	1	1	yes	characteristic
6	C₈×C₂₆₉	C₄	1	1	yes	characteristic
7	C₂×D₂₆₉	Q₈	1	1	yes	characteristic
8	C₄×C₂₆₉	C₂×C₄	1	1	yes	characteristic
9	Dic₂₆₉	D₄	1	1	yes	characteristic
10	C₂×C₂₆₉	C₄⋊C₄	1	1	yes	characteristic
11	D₂₆₉	—	2	1	no	—
12	C₂₆₉	#108	1	1	yes	characteristic, complemented, Sylow
13	#108	—	269	1	no	maximal, Sylow
14	M₁₆	—	269	2	no	—
15	C₂×C₈	—	269	1	no	—
16	C₂×C₄	—	269	1	no	—
17	C₈	—	269	1	no	—
18	C₈	—	538	2	no	—
19	C₈	#11761640	1	1	yes	characteristic
20	C₂²	—	269	1	no	—
21	C₄	—	269	1	no	—
22	C₄	C₂×#11761640	1	1	yes	characteristic
23	C₂	—	538	1	no	—
24	C₂	C₄⋊#11761640	1	1	yes	characteristic

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

N	H ≅ G/N	type
12. C₂₆₉	#108	semidirect