Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1254 conjugacy classes of subgroups; only the 203 normal subgroups are shown.
This group has 1254 conjugacy classes of subgroups — too many to draw. Only its 203 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. #23773427 | C2 | semidirect |
| 2. #23768754 | C2 | semidirect |
| 3. #23762420 | C2 | semidirect |
| 4. #23762352 | C2 | semidirect |
| 5. #23761960 | C2 | semidirect |
| 6. #23761721 | C2 | semidirect |
| 8. C2×C4×Dic158 | C22 | semidirect |
| 9. #19098879 | C22 | semidirect |
| 12. #19098701 | C22 | semidirect |
| 14. #19098616 | C22 | semidirect |
| 15. #19098499 | C22 | semidirect |
| 16. #19098475 | C22 | semidirect |
| 20. #19098429 | C22 | semidirect |
| 21. #19098297 | C22 | semidirect |
| 22. #19098287 | C22 | semidirect |
| 114. C2×D4×C79 | SD16 | semidirect |
| 219. C79 | #18211 | semidirect |
| 313. C2×D4 | #11929612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773427 | 2 |
| #23768754 | 2 |
| #23762420 | 2 |
| #23762352 | 2 |
| #23761960 | 2 |
| #23761721 | 2 |
| C79×#3496 | 2 |
| #18211 | 79 |