Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
564 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23772310 | C2 | semidirect |
| 3. #23765615 | C2 | semidirect |
| 4. #23765612 | C2 | semidirect |
| 5. #23765569 | C2 | semidirect |
| 6. #23765474 | C2 | semidirect |
| 7. #23765346 | C2 | semidirect |
| 8. #23765299 | C2 | semidirect |
| 9. #23765295 | C2 | semidirect |
| 10. #23765209 | C2 | semidirect |
| 11. C79×#2190 | C2 | semidirect |
| 15. #19098960 | C22 | semidirect |
| 16. #19098938 | C22 | semidirect |
| 24. #19098675 | C22 | semidirect |
| 25. #19098674 | C22 | semidirect |
| 30. #19098386 | C22 | semidirect |
| 31. #19098385 | C22 | semidirect |
| 32. #19098383 | C22 | semidirect |
| 33. #19098377 | C22 | semidirect |
| 34. #19098376 | C22 | semidirect |
| 37. #19098340 | C22 | semidirect |
| 132. Q16×C79 | #41 | semidirect |
| 137. D8×C79 | #41 | semidirect |
| 215. #2190 | D79 | semidirect |
| 219. C79 | #33688 | semidirect |
| 319. Q16 | #11929623 | semidirect |
| 326. D8 | #11929623 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774133 | 2 |
| #23772310 | 2 |
| #23765615 | 2 |
| #23765612 | 2 |
| #23765569 | 2 |
| #23765474 | 2 |
| #23765346 | 2 |
| #23765299 | 2 |
| #23765295 | 2 |
| #23765209 | 2 |
| C79×#2190 | 2 |
| #33688 | 79 |