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×#19098998 | C2 | semidirect |
| 2. C22×D1264 | C2 | semidirect |
| 3. #23773887 | C2 | semidirect |
| 4. #23772251 | C2 | semidirect |
| 5. #23765458 | C2 | semidirect |
| 6. #23765434 | C2 | semidirect |
| 7. #23765158 | C2 | semidirect |
| 8. #23765115 | C2 | semidirect |
| 9. C79×#2138 | C2 | semidirect |
| 16. C2×#14579104 | C22 | semidirect |
| 19. C2×#14579102 | C22 | semidirect |
| 22. #19098948 | C22 | semidirect |
| 23. #19098938 | C22 | semidirect |
| 25. #19098645 | C22 | semidirect |
| 28. Dic79⋊C16 | C22 | semidirect |
| 29. #19098363 | C22 | semidirect |
| 33. #358×C79 | C22 | semidirect |
| 34. #357×C79 | C22 | semidirect |
| 44. C2×D632 | D4 | semidirect |
| 190. #2138 | D79 | semidirect |
| 191. C79 | #33585 | semidirect |
| 214. #358 | C2×D79 | 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×#19098998 | 2 |
| C22×D1264 | 2 |
| #23773887 | 2 |
| #23772251 | 2 |
| #23765458 | 2 |
| #23765434 | 2 |
| #23765158 | 2 |
| #23765115 | 2 |
| C79×#2138 | 2 |
| #33585 | 79 |