Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19098386 | C2 | semidirect |
| 5. #23763297 | C2 | semidirect |
| 6. #23761509 | C2 | semidirect |
| 7. C79×#1375 | C2 | semidirect |
| 17. #19098368 | C4 | semidirect |
| 18. #19098365 | C4 | semidirect |
| 155. #1375 | D79 | semidirect |
| 156. C79 | #13143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098386 | 2 |
| C2×#19098374 | 2 |
| #23765113 | 2 |
| #23764293 | 2 |
| #23763297 | 2 |
| #23761509 | 2 |
| C79×#1375 | 2 |
| #13143 | 79 |