Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 141 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. #23757904 | C2 | semidirect |
| 3. #23757578 | C2 | semidirect |
| 4. #23757575 | C2 | semidirect |
| 5. #23757566 | C2 | semidirect |
| 6. #23757551 | C2 | semidirect |
| 7. #23757315 | C2 | semidirect |
| 8. C2×#19097704 | C2 | semidirect |
| 9. #23757301 | C2 | semidirect |
| 64. #41×C157 | Q8 | semidirect |
| 123. C157 | #3083 | semidirect |
| 166. #41 | Dic314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757904 | 2 |
| #23757756 | 2 |
| #23757578 | 2 |
| #23757575 | 2 |
| #23757566 | 2 |
| #23757551 | 2 |
| #23757315 | 2 |
| C2×#19097704 | 2 |
| #23757301 | 2 |
| #23757269 | 2 |
| #417×C157 | 2 |
| #3083 | 157 |