Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
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×#19099574 | C2 | semidirect |
| 2. #23778811 | C2 | semidirect |
| 3. #23778810 | C2 | semidirect |
| 4. #23778806 | C2 | semidirect |
| 5. #23778805 | C2 | semidirect |
| 6. #23778800 | C2 | semidirect |
| 7. C2×#19099558 | C2 | semidirect |
| 8. C2×#41×C317 | C2 | semidirect |
| 12. #19099574 | C22 | semidirect |
| 13. C2×Dic634 | C22 | semidirect |
| 14. C2×D1268 | C22 | semidirect |
| 17. #19099564 | C22 | semidirect |
| 18. #19099562 | C22 | semidirect |
| 19. #19099561 | C22 | semidirect |
| 20. #19099559 | C22 | semidirect |
| 21. #19099558 | C22 | semidirect |
| 22. #19099558 | C22 | semidirect |
| 23. C2×#14579261 | C22 | semidirect |
| 27. #41×C317 | C22 | semidirect |
| 28. C2×Q8×C317 | C22 | semidirect |
| 30. C2×D4×C317 | C22 | semidirect |
| 81. C317 | #575 | semidirect |
| 84. C2×#41 | D317 | semidirect |
| 98. #41 | C2×D317 | semidirect |
| 100. C2×Q8 | C2×D317 | semidirect |
| 104. C2×D4 | C2×D317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099574 | 2 |
| #23778811 | 2 |
| #23778810 | 2 |
| #23778806 | 2 |
| #23778805 | 2 |
| #23778800 | 2 |
| C2×#19099558 | 2 |
| C2×#41×C317 | 2 |
| #575 | 317 |