Subgroups — #37558501

Order 23824.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26045522	C₂	1	2	yes	maximal, complemented
2	C₂×Dic₁₄₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₄₈₉	C₄	1	1	yes	characteristic
4	Dic₁₄₈₉	C₄	1	1	yes	characteristic
5	Dic₁₄₈₉	C₂²	1	1	yes	characteristic
6	C₂×C₁₄₈₉	—	2	1	no	—
7	C₂×C₁₄₈₉	C₂×C₄	1	1	yes	characteristic
8	C₁₄₈₉	M₁₆	1	1	yes	characteristic, complemented, Sylow
9	M₁₆	—	1489	1	no	maximal, Sylow
10	C₂×C₄	—	1489	1	no	—
11	C₈	—	1489	2	no	—
12	C₂²	#20238494	1	1	yes	characteristic
13	C₄	—	1489	1	no	—
14	C₄	—	1489	1	no	—
15	C₂	—	2	1	no	—
16	C₂	C₂×#20238494	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. #26045522	C₂	semidirect
8. C₁₄₈₉	M₁₆	semidirect

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