Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#19097819 | C2 | semidirect |
| 2. #23758071 | C2 | semidirect |
| 3. #23757455 | C2 | semidirect |
| 4. #23757445 | C2 | semidirect |
| 5. #23757291 | C2 | semidirect |
| 6. C2×#19097690 | C2 | semidirect |
| 7. #536×C157 | C2 | semidirect |
| 15. #19097802 | C22 | semidirect |
| 17. #19097797 | C22 | semidirect |
| 21. #19097699 | C22 | semidirect |
| 22. #19097690 | C22 | semidirect |
| 25. C4⋊Q8×C157 | C22 | semidirect |
| 26. #124×C157 | C22 | semidirect |
| 123. C157 | #3020 | semidirect |
| 127. #536 | D157 | semidirect |
| 147. C4⋊Q8 | C2×D157 | semidirect |
| 148. #124 | C2×D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097819 | 2 |
| #23758071 | 2 |
| #23757455 | 2 |
| #23757445 | 2 |
| #23757291 | 2 |
| C2×#19097690 | 2 |
| #536×C157 | 2 |
| #3020 | 157 |