Subgroups — Dic₂₃⋊C₄ #67269

Order 368.

26 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	1	yes	maximal, characteristic
3	C₂×Dic₂₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₂₃	C₂²	1	1	yes	characteristic
5	C₄×C₂₃	—	2	1	no	—
6	Dic₂₃	—	2	1	no	—
7	Dic₂₃	C₄	1	2	yes	complemented
8	C₂×C₂₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₂₃	D₄	1	1	yes	characteristic
10	C₂×C₂₃	Q₈	1	1	yes	characteristic
11	C₂₃	C₄⋊C₄	1	1	yes	characteristic, complemented, Sylow
12	C₄⋊C₄	—	23	1	no	maximal, Sylow
13	C₂×C₄	—	23	1	no	—
14	C₂×C₄	—	23	1	no	—
15	C₂×C₄	D₂₃	1	1	yes	characteristic
16	C₂²	C₂×D₂₃	1	1	yes	characteristic
17	C₄	—	2	1	no	—
18	C₄	—	23	2	no	—
19	C₄	—	46	1	no	—
20	C₂	Dic₄₆	1	1	yes	characteristic
21	C₂	C₄×D₂₃	1	1	yes	characteristic
22	C₂	C₂²⋊D₂₃	1	1	yes	characteristic

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

N	H ≅ G/N	type
7. Dic₂₃	C₄	semidirect
11. C₂₃	C₄⋊C₄	semidirect

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