Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
2222 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2222 conjugacy classes of subgroups — too many to draw. Only its 667 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. #23769360 | C2 | direct (N × H) |
| 2. C2×#19098492 | C2 | semidirect |
| 3. C2×#19098487 | C2 | semidirect |
| 5. C2×#19098461 | C2 | semidirect |
| 6. C2×#376×C79 | C2 | semidirect |
| 12. #19098492 | C22 | semidirect |
| 13. #19098487 | C22 | semidirect |
| 15. #19098461 | C22 | semidirect |
| 18. #376×C79 | C22 | semidirect |
| 107. C2×C79 | #2644 | semidirect |
| 117. C2×#376 | D79 | semidirect |
| 118. C79 | C2×#2644 | semidirect |
| 129. #376 | C2×D79 | semidirect |
| 219. C2 | #23769360 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769360 | 2 |
| C2×#19098492 | 2 |
| C2×#19098487 | 2 |
| C2×#19098465 | 2 |
| C2×#19098461 | 2 |
| C2×#376×C79 | 2 |
| C2×#2644 | 79 |