Finite Group DatabasebetaFinite Group DatabasebetaOrder 20096.
484 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×#19097794 | C2 | semidirect |
| 2. C2×#19097793 | C2 | semidirect |
| 3. #23757925 | C2 | semidirect |
| 4. #23757651 | C2 | semidirect |
| 5. #23757515 | C2 | semidirect |
| 6. #23757477 | C2 | semidirect |
| 7. #23757438 | C2 | semidirect |
| 8. #23757433 | C2 | semidirect |
| 9. #23757355 | C2 | semidirect |
| 10. C8×C22⋊D157 | C2 | semidirect |
| 11. #467×C157 | C2 | semidirect |
| 58. D1256 | D4 | semidirect |
| 129. Dic157 | #135 | semidirect |
| 136. C157 | #3283 | semidirect |
| 143. #467 | D157 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097794 | 2 |
| C2×#19097793 | 2 |
| #23757925 | 2 |
| #23757651 | 2 |
| #23757515 | 2 |
| #23757477 | 2 |
| #23757438 | 2 |
| #23757433 | 2 |
| #23757355 | 2 |
| C8×C22⋊D157 | 2 |
| #467×C157 | 2 |
| #3283 | 157 |