Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
326 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 4. #23761576 | C2 | semidirect |
| 5. #23761575 | C2 | semidirect |
| 6. #23761574 | C2 | semidirect |
| 7. C79×#1414 | C2 | semidirect |
| 8. #19099119 | C4 | semidirect |
| 10. #19098920 | C4 | semidirect |
| 11. #19098918 | C4 | semidirect |
| 19. C4×C8×D79 | C4 | semidirect |
| 165. #1414 | D79 | semidirect |
| 166. C79 | #13602 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773721 | 2 |
| #23765082 | 2 |
| #23765064 | 2 |
| #23761576 | 2 |
| #23761575 | 2 |
| #23761574 | 2 |
| C79×#1414 | 2 |
| #13602 | 79 |