Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1132 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1132 conjugacy classes of subgroups — too many to draw. Only its 179 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. #23774315 | C2 | semidirect |
| 2. #23773853 | C2 | semidirect |
| 3. #23762483 | C2 | semidirect |
| 4. #23762454 | C2 | semidirect |
| 5. #23762062 | C2 | semidirect |
| 6. #23761817 | C2 | semidirect |
| 7. C79×#3549 | C2 | semidirect |
| 9. C2×#14579158 | C22 | semidirect |
| 13. #19098937 | C22 | semidirect |
| 15. #19098758 | C22 | semidirect |
| 17. #19098616 | C22 | semidirect |
| 18. C4×#11929608 | C22 | semidirect |
| 19. #19098312 | C22 | semidirect |
| 20. #19098307 | C22 | semidirect |
| 21. D4⋊(C79⋊C8) | C22 | semidirect |
| 24. #555×C79 | C22 | semidirect |
| 26. D42×C79 | C22 | semidirect |
| 180. #3549 | D79 | semidirect |
| 187. C79 | #18714 | semidirect |
| 191. #555 | C2×D79 | semidirect |
| 193. D42 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774315 | 2 |
| #23773853 | 2 |
| #23762483 | 2 |
| #23762454 | 2 |
| #23762062 | 2 |
| #23761817 | 2 |
| C79×#3549 | 2 |
| #18714 | 79 |