Finite Group DatabasebetaFinite Group DatabasebetaOrder 20288.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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×Q8×D317 | C2 | semidirect |
| 3. C2×#19099563 | C2 | semidirect |
| 4. C2×#19099562 | C2 | semidirect |
| 5. C2×#19099561 | C2 | semidirect |
| 6. SD16×D317 | C2 | direct (N × H) |
| 7. C2×C8×D317 | C2 | semidirect |
| 8. C2×SD16×C317 | C2 | semidirect |
| 11. C2×Dic634 | C22 | semidirect |
| 13. Q8×D317 | C22 | semidirect |
| 20. #19099563 | C22 | semidirect |
| 21. #19099562 | C22 | semidirect |
| 22. #19099561 | C22 | semidirect |
| 23. C2×#14579261 | C22 | semidirect |
| 24. C8×D317 | C22 | semidirect |
| 25. C2×Q8×C317 | C22 | semidirect |
| 27. SD16×C317 | C22 | semidirect |
| 28. C2×C8×C317 | C22 | semidirect |
| 35. Dic634 | C23 | semidirect |
| 44. #14579261 | C23 | semidirect |
| 47. Q8×C317 | C23 | semidirect |
| 52. C8×C317 | C23 | semidirect |
| 59. C2×D317 | SD16 | direct (N × H) |
| 67. C2×C317 | C2×SD16 | semidirect |
| 70. D317 | C2×SD16 | direct (N × H) |
| 71. C317 | C22×SD16 | semidirect |
| 79. C2×SD16 | D317 | direct (N × H) |
| 86. C2×Q8 | C2×D317 | semidirect |
| 97. SD16 | C2×D317 | direct (N × H) |
| 100. C2×C8 | C2×D317 | semidirect |
| 110. Q8 | C22×D317 | semidirect |
| 124. C8 | C22×D317 | semidirect |
| 141. C2 | SD16×D317 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×D317 | 2 |
| C2×D4×D317 | 2 |
| C2×#19099563 | 2 |
| C2×#19099562 | 2 |
| C2×#19099561 | 2 |
| SD16×D317 | 2 |
| C2×C8×D317 | 2 |
| C2×SD16×C317 | 2 |
| C22×SD16 | 317 |