Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
470 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. #23772054 | C2 | semidirect |
| 3. #23763492 | C2 | semidirect |
| 5. #23761306 | C2 | semidirect |
| 6. #23761288 | C2 | semidirect |
| 16. #19098603 | C4 | semidirect |
| 17. #19098603 | C4 | semidirect |
| 19. #19098568 | C4 | semidirect |
| 20. #19098568 | C4 | semidirect |
| 230. C79 | #9348 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773336 | 2 |
| #23772054 | 2 |
| #23763492 | 2 |
| #23761760 | 2 |
| #23761306 | 2 |
| #23761288 | 2 |
| C79×#1519 | 2 |
| #9348 | 79 |