Finite Group DatabasebetaFinite Group DatabasebetaOrder 20032.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 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. C2×#19097561 | C2 | semidirect |
| 2. #23756528 | C2 | semidirect |
| 3. #23756527 | C2 | semidirect |
| 4. #23756523 | C2 | semidirect |
| 5. #23756522 | C2 | semidirect |
| 6. #23756517 | C2 | semidirect |
| 7. C2×#19097545 | C2 | semidirect |
| 8. C2×#41×C313 | C2 | semidirect |
| 12. #19097561 | C22 | semidirect |
| 13. C2×Dic626 | C22 | semidirect |
| 14. C2×D1252 | C22 | semidirect |
| 17. #19097551 | C22 | semidirect |
| 18. #19097549 | C22 | semidirect |
| 19. #19097548 | C22 | semidirect |
| 20. #19097546 | C22 | semidirect |
| 21. #19097545 | C22 | semidirect |
| 22. #19097545 | C22 | semidirect |
| 23. C2×#14578809 | C22 | semidirect |
| 27. #41×C313 | C22 | semidirect |
| 28. C2×Q8×C313 | C22 | semidirect |
| 30. C2×D4×C313 | C22 | semidirect |
| 81. C313 | #575 | semidirect |
| 84. C2×#41 | D313 | semidirect |
| 98. #41 | C2×D313 | semidirect |
| 100. C2×Q8 | C2×D313 | semidirect |
| 104. C2×D4 | C2×D313 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19097561 | 2 |
| #23756528 | 2 |
| #23756527 | 2 |
| #23756523 | 2 |
| #23756522 | 2 |
| #23756517 | 2 |
| C2×#19097545 | 2 |
| C2×#41×C313 | 2 |
| #575 | 313 |