Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
736 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 163 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. #23774145 | C2 | semidirect |
| 2. #23774141 | C2 | semidirect |
| 4. #23763062 | C2 | semidirect |
| 5. #23763061 | C2 | semidirect |
| 6. #23763059 | C2 | semidirect |
| 7. #23763011 | C2 | semidirect |
| 8. #23761703 | C2 | semidirect |
| 11. #19098961 | C22 | semidirect |
| 12. #19098959 | C22 | semidirect |
| 13. #19098943 | C22 | semidirect |
| 14. #19098942 | C22 | semidirect |
| 16. #19098915 | C22 | semidirect |
| 17. #19098914 | C22 | semidirect |
| 18. #19098913 | C22 | semidirect |
| 29. #19098285 | C22 | semidirect |
| 30. #19098284 | C22 | semidirect |
| 31. C8×C79⋊C8 | C22 | semidirect |
| 169. C79 | #19753 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774145 | 2 |
| #23774141 | 2 |
| #23773774 | 2 |
| #23763062 | 2 |
| #23763061 | 2 |
| #23763059 | 2 |
| #23763011 | 2 |
| #23761703 | 2 |
| C79×#3138 | 2 |
| #19753 | 79 |