Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 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. #23757830 | C2 | semidirect |
| 2. #23757632 | C2 | semidirect |
| 3. #23757627 | C2 | semidirect |
| 4. #23757282 | C2 | semidirect |
| 6. C4×#14578938 | C2 | semidirect |
| 9. #19097771 | C22 | semidirect |
| 10. #19097763 | C22 | semidirect |
| 14. #19097695 | C22 | semidirect |
| 16. #19097682 | C22 | semidirect |
| 17. C4×#11929434 | C22 | semidirect |
| 83. C157 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757830 | 2 |
| #23757632 | 2 |
| #23757627 | 2 |
| #23757282 | 2 |
| #23757278 | 2 |
| C4×#14578938 | 2 |
| C2×#124×C157 | 2 |
| #3140 | 157 |