Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
372 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23757997 | C2 | semidirect |
| 2. #23757938 | C2 | semidirect |
| 3. #23757634 | C2 | semidirect |
| 4. #23757566 | C2 | semidirect |
| 5. #23757550 | C2 | semidirect |
| 7. #23757475 | C2 | semidirect |
| 8. #23757403 | C2 | semidirect |
| 9. #23757376 | C2 | semidirect |
| 11. #487×C157 | C2 | semidirect |
| 122. C157 | #3367 | semidirect |
| 127. #487 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757997 | 2 |
| #23757938 | 2 |
| #23757634 | 2 |
| #23757566 | 2 |
| #23757550 | 2 |
| #23757491 | 2 |
| #23757475 | 2 |
| #23757403 | 2 |
| #23757376 | 2 |
| C4×D1256 | 2 |
| #487×C157 | 2 |
| #3367 | 157 |