Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
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×D317 | C2 | semidirect |
| 2. #23778812 | C2 | semidirect |
| 3. #23778809 | C2 | semidirect |
| 4. #23778807 | C2 | semidirect |
| 5. #23778804 | C2 | semidirect |
| 6. #23778802 | C2 | semidirect |
| 7. #23778800 | C2 | semidirect |
| 8. C2×#19099557 | C2 | semidirect |
| 9. #135×C317 | C2 | semidirect |
| 12. #19099574 | C22 | semidirect |
| 15. Q8×D317 | C22 | semidirect |
| 17. D4×D317 | C22 | semidirect |
| 20. Dic1268 | C22 | semidirect |
| 21. #19099564 | C22 | semidirect |
| 22. #19099563 | C22 | semidirect |
| 23. #19099562 | C22 | semidirect |
| 24. #19099561 | C22 | semidirect |
| 25. D2536 | C22 | semidirect |
| 26. #19099559 | C22 | semidirect |
| 27. #19099557 | C22 | semidirect |
| 28. #19099557 | C22 | semidirect |
| 29. C2×#14579261 | C22 | semidirect |
| 30. #41×C317 | C22 | semidirect |
| 31. Q16×C317 | C22 | semidirect |
| 32. SD16×C317 | C22 | semidirect |
| 33. D8×C317 | C22 | semidirect |
| 34. C2×C8×C317 | C22 | semidirect |
| 75. C317 | #575 | semidirect |
| 84. #135 | D317 | semidirect |
| 91. #41 | C2×D317 | semidirect |
| 99. Q16 | C2×D317 | semidirect |
| 103. SD16 | C2×D317 | semidirect |
| 106. D8 | C2×D317 | semidirect |
| 110. C2×C8 | C2×D317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D317 | 2 |
| #23778812 | 2 |
| #23778809 | 2 |
| #23778807 | 2 |
| #23778804 | 2 |
| #23778802 | 2 |
| #23778800 | 2 |
| C2×#19099557 | 2 |
| #135×C317 | 2 |
| #575 | 317 |