Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
748 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 163 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. C2×#19099001 | C2 | semidirect |
| 2. C22×#14579102 | C2 | semidirect |
| 3. #23773881 | C2 | semidirect |
| 4. #23772251 | C2 | semidirect |
| 5. #23765454 | C2 | semidirect |
| 6. #23765434 | C2 | semidirect |
| 7. #23765160 | C2 | semidirect |
| 8. #23765105 | C2 | semidirect |
| 9. C79×#2140 | C2 | semidirect |
| 16. C2×#14579106 | C22 | semidirect |
| 17. C2×D1264 | C22 | semidirect |
| 22. #19098946 | C22 | semidirect |
| 23. #19098938 | C22 | semidirect |
| 25. #19098645 | C22 | semidirect |
| 28. Dic79⋊C16 | C22 | semidirect |
| 29. #19098366 | C22 | semidirect |
| 30. #19098363 | C22 | semidirect |
| 34. #357×C79 | C22 | semidirect |
| 45. C2×D632 | D4 | semidirect |
| 189. #2140 | D79 | semidirect |
| 191. C79 | #33585 | semidirect |
| 216. #357 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099001 | 2 |
| C22×#14579102 | 2 |
| #23773881 | 2 |
| #23772251 | 2 |
| #23765454 | 2 |
| #23765434 | 2 |
| #23765160 | 2 |
| #23765105 | 2 |
| C79×#2140 | 2 |
| #33585 | 79 |