Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
398 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #23761510 | C2 | semidirect |
| 5. #23761509 | C2 | semidirect |
| 6. #23761508 | C2 | semidirect |
| 7. C79×#1387 | C2 | semidirect |
| 153. #1387 | D79 | semidirect |
| 154. C79 | #12872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098600 | 2 |
| #23765010 | 2 |
| #23763435 | 2 |
| #23761510 | 2 |
| #23761509 | 2 |
| #23761508 | 2 |
| C79×#1387 | 2 |
| #12872 | 79 |