Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
480 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23761286 | C2 | semidirect |
| 5. #23761285 | C2 | semidirect |
| 6. #23761252 | C2 | semidirect |
| 7. C79×#1284 | C2 | semidirect |
| 14. #19098430 | C4 | semidirect |
| 15. #19098422 | C4 | semidirect |
| 19. #19098408 | C4 | semidirect |
| 20. #95×D79 | C4 | semidirect |
| 219. #1284 | D79 | semidirect |
| 220. C79 | #8777 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23766337 | 2 |
| C4×#14579075 | 2 |
| #23761736 | 2 |
| #23761286 | 2 |
| #23761285 | 2 |
| #23761252 | 2 |
| C79×#1284 | 2 |
| #8777 | 79 |