Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
106 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 2. #23756505 | C2 | semidirect |
| 3. #23756504 | C2 | semidirect |
| 4. #23756432 | C2 | semidirect |
| 5. #23756425 | C2 | semidirect |
| 6. C4×#14578809 | C2 | semidirect |
| 7. #104×C313 | C2 | semidirect |
| 9. #19097551 | C4 | semidirect |
| 10. #19097549 | C4 | semidirect |
| 11. #19097548 | C4 | semidirect |
| 12. #19097546 | C4 | semidirect |
| 51. C313 | #443 | semidirect |
| 58. #104 | D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23756517 | 2 |
| #23756505 | 2 |
| #23756504 | 2 |
| #23756432 | 2 |
| #23756425 | 2 |
| C4×#14578809 | 2 |
| #104×C313 | 2 |
| #443 | 313 |