Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1082 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1082 conjugacy classes of subgroups — too many to draw. Only its 179 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. #23774778 | C2 | semidirect |
| 2. #23773826 | C2 | semidirect |
| 3. #23762545 | C2 | semidirect |
| 4. #23762516 | C2 | semidirect |
| 5. #23762483 | C2 | semidirect |
| 6. #23762454 | C2 | semidirect |
| 7. #23762135 | C2 | semidirect |
| 8. #23761851 | C2 | semidirect |
| 9. C79×#3549 | C2 | semidirect |
| 11. #19099113 | C22 | semidirect |
| 13. #19098942 | C22 | semidirect |
| 15. #19098937 | C22 | semidirect |
| 17. #19098853 | C22 | semidirect |
| 20. #19098758 | C22 | semidirect |
| 22. #19098587 | C22 | semidirect |
| 23. C2×C4×C79⋊C8 | C22 | semidirect |
| 24. #19098312 | C22 | semidirect |
| 26. D4⋊(C79⋊C8) | C22 | semidirect |
| 27. D4⋊(C79⋊C8) | C22 | semidirect |
| 206. #3549 | D79 | semidirect |
| 215. C79 | #18686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774778 | 2 |
| #23773826 | 2 |
| #23762545 | 2 |
| #23762516 | 2 |
| #23762483 | 2 |
| #23762454 | 2 |
| #23762135 | 2 |
| #23761851 | 2 |
| C79×#3549 | 2 |
| #18686 | 79 |