Subgroups — C₂×C₂²⋊D₂₃ #67294

Order 368.

54 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₂₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×D₂₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²⋊D₂₃	C₂	1	4	yes	maximal, direct product factor
4	C₂×Dic₂₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₂₃	—	2	2	no	—
6	C₂²×C₂₃	C₂²	1	1	yes	characteristic
7	C₂²×C₂₃	C₂²	1	2	yes	complemented
8	C₂×D₂₃	—	2	2	no	—
9	C₂×D₂₃	C₂²	1	2	yes	complemented
10	Dic₂₃	C₂²	1	2	yes	complemented
11	C₂×C₂₃	—	2	2	no	—
12	C₂×C₂₃	D₄	1	2	yes	complemented
13	C₂×C₂₃	C₂³	1	1	yes	characteristic
14	D₂₃	—	2	2	no	—
15	C₂₃	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
16	C₂×D₄	—	23	1	no	maximal, Sylow
17	C₂³	—	23	1	no	—
18	C₂³	D₂₃	1	1	yes	characteristic, complemented
19	D₄	—	23	4	no	—
20	C₂×C₄	—	23	1	no	—
21	C₂²	—	2	2	no	—
22	C₂²	—	23	2	no	—
23	C₂²	—	46	2	no	—
24	C₂²	C₂×D₂₃	1	1	yes	characteristic
25	C₂²	C₂×D₂₃	1	2	yes	complemented
26	C₄	—	23	2	no	—
27	C₂	—	2	2	no	—
28	C₂	—	46	2	no	—
29	C₂	C₂²⋊D₂₃	1	2	yes	direct product factor
30	C₂	C₂²×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.