Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
472 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 4. #23761280 | C2 | semidirect |
| 5. #23761278 | C2 | semidirect |
| 6. #23761267 | C2 | semidirect |
| 7. C79×#1289 | C2 | semidirect |
| 14. #19098430 | C4 | semidirect |
| 15. #19098425 | C4 | semidirect |
| 18. #19098410 | C4 | semidirect |
| 19. #19098408 | C4 | semidirect |
| 234. #1289 | D79 | semidirect |
| 235. C79 | #8762 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766342 | 2 |
| #23763385 | 2 |
| #23761716 | 2 |
| #23761280 | 2 |
| #23761278 | 2 |
| #23761267 | 2 |
| C79×#1289 | 2 |
| #8762 | 79 |