Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
262 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 99 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. #41×D313 | C2 | semidirect |
| 2. #23756529 | C2 | semidirect |
| 3. #23756526 | C2 | semidirect |
| 4. #23756524 | C2 | semidirect |
| 5. #23756521 | C2 | semidirect |
| 6. #23756519 | C2 | semidirect |
| 7. #23756517 | C2 | semidirect |
| 8. C2×#19097544 | C2 | semidirect |
| 9. #135×C313 | C2 | semidirect |
| 12. #19097561 | C22 | semidirect |
| 15. Q8×D313 | C22 | semidirect |
| 17. D4×D313 | C22 | semidirect |
| 20. Dic1252 | C22 | semidirect |
| 21. #19097551 | C22 | semidirect |
| 22. #19097550 | C22 | semidirect |
| 23. #19097549 | C22 | semidirect |
| 24. #19097548 | C22 | semidirect |
| 25. D2504 | C22 | semidirect |
| 26. #19097546 | C22 | semidirect |
| 27. #19097544 | C22 | semidirect |
| 28. #19097544 | C22 | semidirect |
| 29. C2×#14578809 | C22 | semidirect |
| 30. #41×C313 | C22 | semidirect |
| 31. Q16×C313 | C22 | semidirect |
| 32. SD16×C313 | C22 | semidirect |
| 33. D8×C313 | C22 | semidirect |
| 34. C2×C8×C313 | C22 | semidirect |
| 75. C313 | #575 | semidirect |
| 84. #135 | D313 | semidirect |
| 91. #41 | C2×D313 | semidirect |
| 99. Q16 | C2×D313 | semidirect |
| 103. SD16 | C2×D313 | semidirect |
| 106. D8 | C2×D313 | semidirect |
| 110. C2×C8 | C2×D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D313 | 2 |
| #23756529 | 2 |
| #23756526 | 2 |
| #23756524 | 2 |
| #23756521 | 2 |
| #23756519 | 2 |
| #23756517 | 2 |
| C2×#19097544 | 2 |
| #135×C313 | 2 |
| #575 | 313 |