Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
| 3. #23757615 | C2 | semidirect |
| 4. #23757569 | C2 | semidirect |
| 5. #23757564 | C2 | semidirect |
| 6. #23757484 | C2 | semidirect |
| 7. #23757479 | C2 | semidirect |
| 9. #23757381 | C2 | semidirect |
| 10. #23757375 | C2 | semidirect |
| 11. #432×C157 | C2 | semidirect |
| 136. C157 | #3116 | semidirect |
| 148. #432 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757830 | 2 |
| C4×#14578954 | 2 |
| #23757615 | 2 |
| #23757569 | 2 |
| #23757564 | 2 |
| #23757484 | 2 |
| #23757479 | 2 |
| #23757437 | 2 |
| #23757381 | 2 |
| #23757375 | 2 |
| #432×C157 | 2 |
| #3116 | 157 |