Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
272 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 19. #367×C79 | C4 | semidirect |
| 20. #366×C79 | C4 | semidirect |
| 129. C79 | #13118 | semidirect |
| 139. #367 | Dic79 | semidirect |
| 140. #366 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764139 | 2 |
| #23763286 | 2 |
| #23761508 | 2 |
| #23761505 | 2 |
| #23761499 | 2 |
| #23761479 | 2 |
| C79×#2159 | 2 |
| #13118 | 79 |