Subgroups — #67267

Order 368.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₂₃	C₂	1	1	yes	maximal, characteristic
2	C₂₃⋊C₈	C₂	1	2	yes	maximal, complemented
3	C₂²×C₂₃	C₄	1	1	yes	characteristic
4	C₄×C₂₃	C₄	1	1	yes	characteristic
5	C₄×C₂₃	C₂²	1	1	yes	characteristic
6	C₂×C₂₃	—	2	1	no	—
7	C₂×C₂₃	C₂×C₄	1	1	yes	characteristic
8	C₂₃	M₁₆	1	1	yes	characteristic, complemented, Sylow
9	M₁₆	—	23	1	no	maximal, Sylow
10	C₂×C₄	D₂₃	1	1	yes	characteristic
11	C₈	—	23	2	no	—
12	C₂²	Dic₂₃	1	1	yes	characteristic
13	C₄	Dic₂₃	1	1	yes	characteristic
14	C₄	C₂×D₂₃	1	1	yes	characteristic
15	C₂	—	2	1	no	—
16	C₂	C₂×Dic₂₃	1	1	yes	characteristic

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

N	H ≅ G/N	type
2. C₂₃⋊C₈	C₂	semidirect
8. C₂₃	M₁₆	semidirect

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