Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
302 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 85 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. C2×#19098387 | C2 | semidirect |
| 5. #23761508 | C2 | semidirect |
| 6. #23761499 | C2 | semidirect |
| 7. C79×#1387 | C2 | semidirect |
| 149. #1387 | D79 | semidirect |
| 151. C79 | #13501 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098387 | 2 |
| C2×#19098344 | 2 |
| #23763439 | 2 |
| #23763434 | 2 |
| #23761508 | 2 |
| #23761499 | 2 |
| C79×#1387 | 2 |
| #13501 | 79 |