Subgroups — C₄×Dic₂₃ #67268

Order 368.

30 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	C₂×Dic₂₃	C₂	1	2	yes	maximal
3	C₂²×C₂₃	C₂²	1	1	yes	characteristic
4	C₄×C₂₃	C₄	1	2	yes	complemented
5	Dic₂₃	C₄	1	4	yes	direct product factor
6	C₂×C₂₃	C₂×C₄	1	2	yes	—
7	C₂×C₂₃	C₂×C₄	1	1	yes	characteristic
8	C₂₃	C₄²	1	1	yes	characteristic, complemented, Sylow
9	C₄²	—	23	1	no	maximal, Sylow
10	C₂×C₄	—	23	2	no	—
11	C₂×C₄	D₂₃	1	1	yes	characteristic
12	C₂²	C₂×D₂₃	1	1	yes	characteristic
13	C₄	—	23	4	no	—
14	C₄	Dic₂₃	1	2	yes	direct product factor
15	C₂	C₄×D₂₃	1	2	yes	—
16	C₂	C₂×Dic₂₃	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.