Subgroups — C₂³×Dic₂₂₃ #20297339

Order 7136.

236 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Dic₂₂₃	C₂	1	14	yes	maximal, direct product factor
2	C₂⁴×C₂₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×Dic₂₂₃	C₂²	1	28	yes	direct product factor
4	C₂³×C₂₂₃	C₄	1	8	yes	complemented
5	C₂³×C₂₂₃	C₂²	1	7	yes	—
6	C₂²×C₂₂₃	C₂×C₄	1	28	yes	complemented
7	C₂²×C₂₂₃	C₂³	1	7	yes	—
8	Dic₂₂₃	C₂³	1	8	yes	direct product factor
9	C₂×C₂₂₃	C₂²×C₄	1	14	yes	complemented
10	C₂×C₂₂₃	C₂⁴	1	1	yes	characteristic
11	C₂₂₃	C₂³×C₄	1	1	yes	characteristic, complemented, Sylow
12	C₂³×C₄	—	223	1	no	maximal, Sylow
13	C₂⁴	D₂₂₃	1	1	yes	characteristic
14	C₂²×C₄	—	223	14	no	—
15	C₂³	Dic₂₂₃	1	8	yes	direct product factor
16	C₂³	C₂×D₂₂₃	1	7	yes	—
17	C₂×C₄	—	223	28	no	—
18	C₂²	C₂×Dic₂₂₃	1	28	yes	direct product factor
19	C₂²	C₂²×D₂₂₃	1	7	yes	—
20	C₄	—	223	8	no	—
21	C₂	C₂²×Dic₂₂₃	1	14	yes	direct product factor
22	C₂	C₂³×D₂₂₃	1	1	yes	characteristic

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