Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
640 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 640 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23771881 | C2 | semidirect |
| 3. #23765092 | C2 | semidirect |
| 4. #23763373 | C2 | semidirect |
| 5. #23761528 | C2 | semidirect |
| 6. #23761522 | C2 | semidirect |
| 7. C79×#2122 | C2 | semidirect |
| 9. C2×#14579187 | C4 | semidirect |
| 10. C22×#11929612 | C4 | semidirect |
| 18. #19098571 | C4 | semidirect |
| 19. #19098557 | C4 | semidirect |
| 249. #2122 | D79 | semidirect |
| 253. C79 | #13098 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772684 | 2 |
| #23771881 | 2 |
| #23765092 | 2 |
| #23763373 | 2 |
| #23761528 | 2 |
| #23761522 | 2 |
| C79×#2122 | 2 |
| #13098 | 79 |