Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
472 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#19097801 | C2 | semidirect |
| 2. C2×#19097777 | C2 | semidirect |
| 4. #23757849 | C2 | semidirect |
| 5. #23757530 | C2 | semidirect |
| 6. #23757518 | C2 | semidirect |
| 7. #23757513 | C2 | semidirect |
| 8. #23757501 | C2 | semidirect |
| 9. #23757316 | C2 | semidirect |
| 10. C2×#19097696 | C2 | semidirect |
| 11. #416×C157 | C2 | semidirect |
| 58. #14578938 | D4 | semidirect |
| 143. C157 | #3063 | semidirect |
| 154. #416 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097801 | 2 |
| C2×#19097777 | 2 |
| #23757851 | 2 |
| #23757849 | 2 |
| #23757530 | 2 |
| #23757518 | 2 |
| #23757513 | 2 |
| #23757501 | 2 |
| #23757316 | 2 |
| C2×#19097696 | 2 |
| #416×C157 | 2 |
| #3063 | 157 |