Subgroups — #20297273

Order 7136.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₂²⋊D₂₂₃	C₂	1	3	yes	maximal, complemented
2	C₂²⋊Dic₂₂₃	C₂	1	3	yes	maximal, complemented
3	C₂⁴×C₂₂₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₂₂₃	C₂²	1	1	yes	characteristic, complemented
5	C₂²⋊D₂₂₃	—	2	6	no	—
6	C₂×Dic₂₂₃	C₂²	1	3	yes	complemented
7	C₂³×C₂₂₃	—	2	6	no	—
8	C₂³×C₂₂₃	C₂²	1	3	yes	—
9	C₂²×C₂₂₃	—	2	8	no	—
10	C₂²×C₂₂₃	—	2	6	no	—
11	C₂²×C₂₂₃	D₄	1	6	yes	complemented
12	C₂²×C₂₂₃	C₂³	1	1	yes	characteristic
13	C₂×D₂₂₃	—	2	3	no	—
14	Dic₂₂₃	—	2	3	no	—
15	C₂×C₂₂₃	—	2	6	no	—
16	C₂×C₂₂₃	C₂×D₄	1	3	yes	—
17	D₂₂₃	—	4	1	no	—
18	C₂₂₃	#120	1	1	yes	characteristic, complemented, Sylow
19	#120	—	223	1	no	maximal, Sylow
20	C₂⁴	D₂₂₃	1	1	yes	characteristic, complemented
21	C₂×D₄	—	223	3	no	—
22	C₂²⋊C₄	—	223	3	no	—
23	C₂³	—	2	6	no	—
24	C₂³	—	223	1	no	—
25	C₂³	C₂×D₂₂₃	1	3	yes	—
26	D₄	—	446	6	no	—
27	C₂×C₄	—	223	3	no	—
28	C₂²	—	2	8	no	—
29	C₂²	—	2	6	no	—
30	C₂²	—	446	3	no	—
31	C₂²	C₂²⋊D₂₂₃	1	6	yes	complemented
32	C₂²	C₂²×D₂₂₃	1	1	yes	characteristic
33	C₄	—	446	3	no	—
34	C₂	—	2	6	no	—
35	C₂	—	892	1	no	—
36	C₂	C₂×C₂²⋊D₂₂₃	1	3	yes	—

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