Subgroups — #67262

Order 368.

20 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₂₃	C₂	1	1	yes	maximal, characteristic
2	C₈×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₂₃	C₄	1	1	yes	characteristic
5	C₄×C₂₃	C₂²	1	1	yes	characteristic
6	Dic₂₃	C₄	1	1	yes	characteristic
7	C₂×C₂₃	C₂×C₄	1	1	yes	characteristic
8	D₂₃	—	2	1	no	—
9	C₂₃	M₁₆	1	1	yes	characteristic, complemented, Sylow
10	M₁₆	—	23	1	no	maximal, Sylow
11	C₂×C₄	—	23	1	no	—
12	C₈	—	23	1	no	—
13	C₈	D₂₃	1	1	yes	characteristic, complemented
14	C₂²	—	23	1	no	—
15	C₄	—	23	1	no	—
16	C₄	C₂×D₂₃	1	1	yes	characteristic
17	C₂	—	46	1	no	—
18	C₂	C₄×D₂₃	1	1	yes	characteristic

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

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