Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
712 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 712 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×#19099003 | C2 | semidirect |
| 2. C22×#14579106 | C2 | semidirect |
| 4. #23772267 | C2 | semidirect |
| 5. #23765465 | C2 | semidirect |
| 6. #23765439 | C2 | semidirect |
| 7. #23765158 | C2 | semidirect |
| 8. #23765115 | C2 | semidirect |
| 9. C79×#2138 | C2 | semidirect |
| 16. C2×#14579107 | C22 | semidirect |
| 19. C2×#14579105 | C22 | semidirect |
| 25. #19098657 | C22 | semidirect |
| 28. Dic79⋊C16 | C22 | semidirect |
| 33. #358×C79 | C22 | semidirect |
| 34. #357×C79 | C22 | semidirect |
| 40. C2×Dic316 | D4 | semidirect |
| 185. #2138 | D79 | semidirect |
| 186. C79 | #33587 | semidirect |
| 209. #358 | C2×D79 | semidirect |
| 211. #357 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099003 | 2 |
| C22×#14579106 | 2 |
| #23773887 | 2 |
| #23772267 | 2 |
| #23765465 | 2 |
| #23765439 | 2 |
| #23765158 | 2 |
| #23765115 | 2 |
| C79×#2138 | 2 |
| #33587 | 79 |