Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
782 conjugacy classes of subgroups.
The subgroup lattice has 606 nodes — too large to display as a diagram.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #23761520 | C2 | direct (N × H) |
| 5. C22×#11929608 | C4 | semidirect |
| 6. C23×C79⋊C8 | C4 | semidirect |
| 10. #19098537 | C4 | semidirect |
| 13. C2×#14579076 | C4 | semidirect |
| 16. #19098530 | C4 | semidirect |
| 24. #410×C79 | C4 | semidirect |
| 27. C2×#99×C79 | C4 | semidirect |
| 31. C2×#11929608 | C2×C4 | semidirect |
| 37. C22×C79⋊C8 | C2×C4 | semidirect |
| 48. #14579076 | C2×C4 | semidirect |
| 82. #99×C79 | C2×C4 | semidirect |
| 301. C2×C79 | #1391 | semidirect |
| 307. C79 | C2×#1391 | semidirect |
| 319. #410 | Dic79 | semidirect |
| 324. C2×#99 | Dic79 | semidirect |
| 381. #99 | C2×Dic79 | semidirect |
| 603. C2 | #23761520 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098537 | 2 |
| C2×#19098530 | 2 |
| #23761520 | 2 |
| C2×#410×C79 | 2 |
| C2×#1391 | 79 |