Subgroups — C₂²⋊C₄×C₂₃ #67278

Order 368.

34 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
2	C₂×C₄×C₂₃	C₂	1	2	yes	maximal, complemented
3	C₂²×C₂₃	—	2	2	no	—
4	C₂²×C₂₃	C₄	1	2	yes	complemented
5	C₂²×C₂₃	C₂²	1	1	yes	characteristic
6	C₄×C₂₃	—	2	2	no	—
7	C₂×C₂₃	—	2	2	no	—
8	C₂×C₂₃	C₂×C₄	1	1	yes	characteristic
9	C₂×C₂₃	D₄	1	2	yes	—
10	C₂₃	C₂²⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
11	C₂²⋊C₄	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
12	C₂³	C₂×C₂₃	1	1	yes	characteristic
13	C₂×C₄	C₂×C₂₃	1	2	yes	complemented
14	C₂²	—	2	2	no	—
15	C₂²	C₄×C₂₃	1	2	yes	complemented
16	C₂²	C₂²×C₂₃	1	1	yes	characteristic
17	C₄	—	2	2	no	—
18	C₂	—	2	2	no	—
19	C₂	C₂×C₄×C₂₃	1	1	yes	characteristic
20	C₂	D₄×C₂₃	1	2	yes	—

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.