Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 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 |
| 3. #23757612 | C2 | semidirect |
| 4. #23757550 | C2 | semidirect |
| 5. #23757513 | C2 | semidirect |
| 6. #23757480 | C2 | semidirect |
| 7. #23757438 | C2 | semidirect |
| 8. C4×#14578943 | C2 | semidirect |
| 9. C8×D628 | C2 | semidirect |
| 10. #23757268 | C2 | semidirect |
| 11. #487×C157 | C2 | semidirect |
| 125. C157 | #3302 | semidirect |
| 129. #487 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23757997 | 2 |
| #23757926 | 2 |
| #23757612 | 2 |
| #23757550 | 2 |
| #23757513 | 2 |
| #23757480 | 2 |
| #23757438 | 2 |
| C4×#14578943 | 2 |
| C8×D628 | 2 |
| #23757268 | 2 |
| #487×C157 | 2 |
| #3302 | 157 |