Subgroups — #20297263

Order 7136.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊Dic₂₂₃	C₂	1	2	yes	maximal, complemented
2	C₂²⋊Dic₂₂₃	C₂	1	2	yes	maximal
3	C₄×Dic₂₂₃	C₂	1	2	yes	maximal, complemented
4	C₂²×C₄×C₂₂₃	C₂	1	1	yes	maximal, characteristic
5	C₂×Dic₂₂₃	C₂²	1	4	yes	—
6	C₂³×C₂₂₃	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₂₂₃	C₄	1	4	yes	complemented
8	C₂×C₄×C₂₂₃	C₂²	1	1	yes	characteristic
9	C₂×C₄×C₂₂₃	C₂²	1	1	yes	characteristic
10	C₂²×C₂₂₃	—	2	2	no	—
11	C₂²×C₂₂₃	C₂×C₄	1	2	yes	—
12	C₂²×C₂₂₃	C₂³	1	1	yes	characteristic
13	C₄×C₂₂₃	C₂×C₄	1	2	yes	—
14	C₄×C₂₂₃	C₂×C₄	1	2	yes	—
15	Dic₂₂₃	—	2	4	no	—
16	C₂×C₂₂₃	—	2	2	no	—
17	C₂×C₂₂₃	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₂₂₃	#41	1	2	yes	—
19	C₂₂₃	#117	1	1	yes	characteristic, complemented, Sylow
20	#117	—	223	1	no	maximal, Sylow
21	C₂²×C₄	D₂₂₃	1	1	yes	characteristic
22	C₄⋊C₄	—	223	2	no	—
23	C₂²⋊C₄	—	223	2	no	—
24	C₄²	—	223	2	no	—
25	C₂³	C₂×D₂₂₃	1	1	yes	characteristic
26	C₂×C₄	—	223	4	no	—
27	C₂×C₄	Dic₂₂₃	1	4	yes	complemented
28	C₂×C₄	C₂×D₂₂₃	1	1	yes	characteristic
29	C₂×C₄	C₂×D₂₂₃	1	1	yes	characteristic
30	C₂²	—	2	2	no	—
31	C₂²	C₂×Dic₂₂₃	1	2	yes	—
32	C₂²	C₂²×D₂₂₃	1	1	yes	characteristic
33	C₄	—	446	4	no	—
34	C₄	C₂×Dic₂₂₃	1	2	yes	—
35	C₄	C₂×Dic₂₂₃	1	2	yes	—
36	C₂	—	2	2	no	—
37	C₂	C₂²×Dic₂₂₃	1	1	yes	characteristic
38	C₂	#16813170	1	2	yes	—

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