Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1306 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1306 conjugacy classes of subgroups — too many to draw. Only its 251 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 |
|---|---|---|
| 1. #23778112 | C2 | semidirect |
| 3. #23772106 | C2 | semidirect |
| 4. #23763816 | C2 | semidirect |
| 5. #23763685 | C2 | semidirect |
| 6. #23763203 | C2 | semidirect |
| 7. C79×#1791 | C2 | semidirect |
| 12. C22×#11929607 | C22 | semidirect |
| 18. #19098589 | C22 | semidirect |
| 20. #19098526 | C22 | semidirect |
| 21. #19098521 | C22 | semidirect |
| 22. #19098335 | C22 | semidirect |
| 34. C2×#11929608 | D4 | semidirect |
| 39. C22×C79⋊C8 | D4 | semidirect |
| 150. #1791 | D79 | semidirect |
| 152. C79 | #21484 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23778112 | 2 |
| #23772792 | 2 |
| #23772106 | 2 |
| #23763816 | 2 |
| #23763685 | 2 |
| #23763203 | 2 |
| C79×#1791 | 2 |
| #21484 | 79 |