Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
748 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 171 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×#19098999 | C2 | semidirect |
| 2. #23773881 | C2 | semidirect |
| 3. #23772252 | C2 | semidirect |
| 4. #23765453 | C2 | semidirect |
| 5. #23765433 | C2 | semidirect |
| 6. #23765158 | C2 | semidirect |
| 7. #23765116 | C2 | semidirect |
| 8. #23765108 | C2 | semidirect |
| 9. C22×D16×C79 | C2 | semidirect |
| 15. C2×#14579105 | C22 | semidirect |
| 16. C2×#14579102 | C22 | semidirect |
| 19. #19098946 | C22 | semidirect |
| 20. #19098938 | C22 | semidirect |
| 22. D8×Dic79 | C22 | semidirect |
| 26. Dic79⋊C16 | C22 | semidirect |
| 27. #19098368 | C22 | semidirect |
| 28. #19098365 | C22 | semidirect |
| 29. #19098364 | C22 | semidirect |
| 70. C2×D8×C79 | D4 | semidirect |
| 183. C22×D16 | D79 | semidirect |
| 191. C79 | #33585 | semidirect |
| 233. C2×D8 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098999 | 2 |
| #23773881 | 2 |
| #23772252 | 2 |
| #23765453 | 2 |
| #23765433 | 2 |
| #23765158 | 2 |
| #23765116 | 2 |
| #23765108 | 2 |
| C22×D16×C79 | 2 |
| #33585 | 79 |