Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
564 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 121 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. #23774133 | C2 | semidirect |
| 2. #23772309 | C2 | semidirect |
| 3. #23765614 | C2 | semidirect |
| 4. #23765570 | C2 | semidirect |
| 5. #23765475 | C2 | semidirect |
| 6. #23765348 | C2 | semidirect |
| 7. #23765345 | C2 | semidirect |
| 8. #23765301 | C2 | semidirect |
| 9. #23765297 | C2 | semidirect |
| 10. #23765209 | C2 | semidirect |
| 11. C79×#2238 | C2 | semidirect |
| 17. #19098960 | C22 | semidirect |
| 18. #19098938 | C22 | semidirect |
| 26. #19098675 | C22 | semidirect |
| 27. #19098674 | C22 | semidirect |
| 31. #19098387 | C22 | semidirect |
| 32. #19098383 | C22 | semidirect |
| 33. #19098375 | C22 | semidirect |
| 37. #19098340 | C22 | semidirect |
| 40. #365×C79 | C22 | semidirect |
| 41. #361×C79 | C22 | semidirect |
| 108. Dic316 | #41 | semidirect |
| 113. D632 | #41 | semidirect |
| 211. #2238 | D79 | semidirect |
| 219. C79 | #33688 | semidirect |
| 242. #365 | C2×D79 | semidirect |
| 245. #361 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774133 | 2 |
| #23772309 | 2 |
| #23765614 | 2 |
| #23765570 | 2 |
| #23765475 | 2 |
| #23765348 | 2 |
| #23765345 | 2 |
| #23765301 | 2 |
| #23765297 | 2 |
| #23765209 | 2 |
| C79×#2238 | 2 |
| #33688 | 79 |