Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1716 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1716 conjugacy classes of subgroups — too many to draw. Only its 195 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. #23773850 | C2 | semidirect |
| 2. #23773491 | C2 | semidirect |
| 3. #23762516 | C2 | semidirect |
| 4. #23762454 | C2 | semidirect |
| 5. #23762114 | C2 | semidirect |
| 6. #23761843 | C2 | semidirect |
| 7. C2×D42×C79 | C2 | semidirect |
| 9. #19099113 | C22 | semidirect |
| 11. #19098939 | C22 | semidirect |
| 12. #19098935 | C22 | semidirect |
| 14. #19098853 | C22 | semidirect |
| 15. #19098758 | C22 | semidirect |
| 18. #19098620 | C22 | semidirect |
| 19. C4×#11929608 | C22 | semidirect |
| 20. #19098307 | C22 | semidirect |
| 21. D4⋊(C79⋊C8) | C22 | semidirect |
| 36. #14579161 | C23 | semidirect |
| 37. #14579158 | C23 | semidirect |
| 42. C4⋊(C79⋊C8) | C23 | semidirect |
| 48. C4×C79⋊C8 | C23 | semidirect |
| 139. D4×C79 | AGL(1,ℤ/8) | semidirect |
| 184. C2×D42 | D79 | semidirect |
| 191. C79 | #18524 | semidirect |
| 327. D4 | #14579187 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773850 | 2 |
| #23773491 | 2 |
| #23762516 | 2 |
| #23762454 | 2 |
| #23762114 | 2 |
| #23761843 | 2 |
| C2×D42×C79 | 2 |
| #18524 | 79 |