Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
624 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #23765094 | C2 | semidirect |
| 4. #23765053 | C2 | semidirect |
| 6. #23761523 | C2 | semidirect |
| 7. C79×#1395 | C2 | semidirect |
| 9. C2×#14579194 | C4 | semidirect |
| 10. C22×Dic316 | C4 | semidirect |
| 18. #19098573 | C4 | semidirect |
| 20. #19098560 | C4 | semidirect |
| 244. #1395 | D79 | semidirect |
| 246. C79 | #13096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772697 | 2 |
| #23771881 | 2 |
| #23765094 | 2 |
| #23765053 | 2 |
| #23763373 | 2 |
| #23761523 | 2 |
| C79×#1395 | 2 |
| #13096 | 79 |