Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
292 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23757228 | C2 | semidirect |
| 5. #23757038 | C2 | semidirect |
| 6. #23757033 | C2 | semidirect |
| 7. C2×#97×C157 | C2 | semidirect |
| 10. #19097777 | C4 | semidirect |
| 16. #19097699 | C4 | semidirect |
| 17. #19097696 | C4 | semidirect |
| 18. #19097693 | C4 | semidirect |
| 98. C157 | #1765 | semidirect |
| 104. C2×#97 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097777 | 2 |
| C2×#19097699 | 2 |
| #23757270 | 2 |
| #23757228 | 2 |
| #23757038 | 2 |
| #23757033 | 2 |
| C2×#97×C157 | 2 |
| #1765 | 157 |