Subgroups — #36384697

Order 22768.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₄₂₃⋊C₈	C₂	1	2	yes	maximal, complemented
2	C₂×C₄×C₁₄₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₁₄₂₃	C₄	1	1	yes	characteristic
4	C₄×C₁₄₂₃	C₄	1	1	yes	characteristic
5	C₄×C₁₄₂₃	C₂²	1	1	yes	characteristic
6	C₂×C₁₄₂₃	—	2	1	no	—
7	C₂×C₁₄₂₃	C₂×C₄	1	1	yes	characteristic
8	C₁₄₂₃	M₁₆	1	1	yes	characteristic, complemented, Sylow
9	M₁₆	—	1423	1	no	maximal, Sylow
10	C₂×C₄	D₁₄₂₃	1	1	yes	characteristic
11	C₈	—	1423	2	no	—
12	C₂²	Dic₁₄₂₃	1	1	yes	characteristic
13	C₄	Dic₁₄₂₃	1	1	yes	characteristic
14	C₄	C₂×D₁₄₂₃	1	1	yes	characteristic
15	C₂	—	2	1	no	—
16	C₂	C₂×Dic₁₄₂₃	1	1	yes	characteristic

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

N	H ≅ G/N	type
1. C₁₄₂₃⋊C₈	C₂	semidirect
8. C₁₄₂₃	M₁₆	semidirect

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