Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
258 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23756543 | C2 | semidirect |
| 2. #23756528 | C2 | semidirect |
| 3. #23756522 | C2 | semidirect |
| 4. #23756517 | C2 | semidirect |
| 5. C2×#19097548 | C2 | semidirect |
| 6. #23756504 | C2 | semidirect |
| 7. 2−1+4×C313 | C2 | semidirect |
| 12. #19097551 | C22 | semidirect |
| 13. #19097549 | C22 | semidirect |
| 14. #19097548 | C22 | semidirect |
| 15. #19097548 | C22 | semidirect |
| 16. #19097546 | C22 | semidirect |
| 17. #19097545 | C22 | semidirect |
| 18. C2×#14578809 | C22 | semidirect |
| 21. #41×C313 | C22 | semidirect |
| 23. C2×Q8×C313 | C22 | semidirect |
| 53. C313 | #577 | semidirect |
| 55. 2−1+4 | D313 | semidirect |
| 66. #41 | C2×D313 | semidirect |
| 68. C2×Q8 | C2×D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23756543 | 2 |
| #23756528 | 2 |
| #23756522 | 2 |
| #23756517 | 2 |
| C2×#19097548 | 2 |
| #23756504 | 2 |
| 2−1+4×C313 | 2 |
| #577 | 313 |