Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
668 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 668 conjugacy classes of subgroups — too many to draw. Only its 135 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. #23776537 | C2 | semidirect |
| 2. #23775199 | C2 | semidirect |
| 3. #23765517 | C2 | semidirect |
| 4. #23765473 | C2 | semidirect |
| 5. #23765356 | C2 | semidirect |
| 6. #23765282 | C2 | semidirect |
| 7. #23765238 | C2 | semidirect |
| 8. C79×#2246 | C2 | semidirect |
| 10. #19099364 | C22 | semidirect |
| 11. #19098999 | C22 | semidirect |
| 16. #19098979 | C22 | semidirect |
| 18. #19098830 | C22 | semidirect |
| 21. #19098681 | C22 | semidirect |
| 22. #19098393 | C22 | semidirect |
| 23. #19098384 | C22 | semidirect |
| 24. #19098376 | C22 | semidirect |
| 25. #19098371 | C22 | semidirect |
| 26. #19098346 | C22 | semidirect |
| 27. C2×D16×C79 | C22 | semidirect |
| 28. C2×D16×C79 | C22 | semidirect |
| 29. #493×C79 | C22 | semidirect |
| 30. C4×C16×C79 | C22 | semidirect |
| 44. Dic632 | D4 | semidirect |
| 45. #14579106 | D4 | semidirect |
| 47. D1264 | D4 | semidirect |
| 145. #2246 | D79 | semidirect |
| 151. C79 | #33858 | semidirect |
| 159. C2×D16 | C2×D79 | semidirect |
| 160. C2×D16 | C2×D79 | semidirect |
| 162. #493 | C2×D79 | semidirect |
| 173. C4×C16 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776537 | 2 |
| #23775199 | 2 |
| #23765517 | 2 |
| #23765473 | 2 |
| #23765356 | 2 |
| #23765282 | 2 |
| #23765238 | 2 |
| C79×#2246 | 2 |
| #33858 | 79 |