Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
778 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 143 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. #23775212 | C2 | semidirect |
| 2. #23774999 | C2 | semidirect |
| 3. #23762862 | C2 | semidirect |
| 4. #23762834 | C2 | semidirect |
| 5. #23762632 | C2 | semidirect |
| 6. #23762452 | C2 | semidirect |
| 7. #23762286 | C2 | semidirect |
| 8. C8×D632 | C2 | semidirect |
| 9. C79×#1706 | C2 | semidirect |
| 12. #19099198 | C22 | semidirect |
| 14. #19098840 | C22 | semidirect |
| 17. #19098765 | C22 | semidirect |
| 25. #19098642 | C22 | semidirect |
| 26. C8×D316 | C22 | semidirect |
| 28. #19098316 | C22 | semidirect |
| 29. #19098316 | C22 | semidirect |
| 30. #19098309 | C22 | semidirect |
| 31. #19098307 | C22 | semidirect |
| 32. #19098292 | C22 | semidirect |
| 33. #19098292 | C22 | semidirect |
| 34. #500×C79 | C22 | semidirect |
| 36. #492×C79 | C22 | semidirect |
| 37. #486×C79 | C22 | semidirect |
| 38. C82×C79 | C22 | semidirect |
| 100. D632 | D8 | semidirect |
| 195. #1706 | D79 | semidirect |
| 202. C79 | #19884 | semidirect |
| 206. #500 | C2×D79 | semidirect |
| 208. #492 | C2×D79 | semidirect |
| 209. #486 | C2×D79 | semidirect |
| 231. C82 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23775212 | 2 |
| #23774999 | 2 |
| #23762862 | 2 |
| #23762834 | 2 |
| #23762632 | 2 |
| #23762452 | 2 |
| #23762286 | 2 |
| C8×D632 | 2 |
| C79×#1706 | 2 |
| #19884 | 79 |