Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
452 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 2. #23772570 | C2 | semidirect |
| 3. #23764232 | C2 | semidirect |
| 4. #23761870 | C2 | semidirect |
| 5. #23761293 | C2 | semidirect |
| 6. #23761291 | C2 | semidirect |
| 7. C79×#1500 | C2 | semidirect |
| 9. #19098973 | C4 | semidirect |
| 10. #19098953 | C4 | semidirect |
| 11. #19098929 | C4 | semidirect |
| 12. #19098922 | C4 | semidirect |
| 219. #1500 | D79 | semidirect |
| 223. C79 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773996 | 2 |
| #23772570 | 2 |
| #23764232 | 2 |
| #23761870 | 2 |
| #23761293 | 2 |
| #23761291 | 2 |
| C79×#1500 | 2 |
| #8997 | 79 |