Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
686 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 159 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. #499×D79 | C2 | semidirect |
| 3. #23765643 | C2 | semidirect |
| 4. #23765642 | C2 | semidirect |
| 5. #23765641 | C2 | semidirect |
| 6. #23765640 | C2 | semidirect |
| 7. #357×D79 | C2 | semidirect |
| 8. #346×D79 | C2 | semidirect |
| 9. C79×#2244 | C2 | semidirect |
| 15. #19098965 | C22 | semidirect |
| 16. #19098964 | C22 | semidirect |
| 26. #19098365 | C22 | semidirect |
| 27. #19098364 | C22 | semidirect |
| 28. #19098363 | C22 | semidirect |
| 29. #19098339 | C22 | semidirect |
| 30. #19098338 | C22 | semidirect |
| 31. #499×C79 | C22 | semidirect |
| 33. #357×C79 | C22 | semidirect |
| 34. #346×C79 | C22 | semidirect |
| 155. D79 | #2244 | direct (N × H) |
| 162. #2244 | D79 | direct (N × H) |
| 165. C79 | C2×#2244 | semidirect |
| 175. #499 | C2×D79 | semidirect |
| 187. #357 | C2×D79 | semidirect |
| 190. #346 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D79 | 2 |
| #493×D79 | 2 |
| #23765643 | 2 |
| #23765642 | 2 |
| #23765641 | 2 |
| #23765640 | 2 |
| #357×D79 | 2 |
| #346×D79 | 2 |
| C79×#2244 | 2 |
| C2×#2244 | 79 |