Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
398 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 75 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #23769049 | C2 | semidirect |
| 4. #23761292 | C2 | semidirect |
| 5. #23761264 | C2 | semidirect |
| 6. #23761255 | C2 | semidirect |
| 52. C4⋊Q8×C79 | Q8 | semidirect |
| 53. #127×C79 | Q8 | semidirect |
| 189. C79 | #10378 | semidirect |
| 212. C4⋊Q8 | Dic158 | semidirect |
| 213. #127 | Dic158 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769049 | 2 |
| #23764320 | 2 |
| #23761908 | 2 |
| #23761292 | 2 |
| #23761264 | 2 |
| #23761255 | 2 |
| C79×#1514 | 2 |
| #10378 | 79 |