Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
466 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 127 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. #508×D59 | C2 | semidirect |
| 2. #21426415 | C2 | semidirect |
| 3. #21426412 | C2 | semidirect |
| 4. #21426410 | C2 | semidirect |
| 5. #21426407 | C2 | semidirect |
| 6. #21426405 | C2 | semidirect |
| 7. #21426403 | C2 | semidirect |
| 8. C2×#16837235 | C2 | semidirect |
| 9. C59×#2262 | C2 | semidirect |
| 12. #16837834 | C22 | semidirect |
| 16. Q32×D59 | C22 | semidirect |
| 18. D16×D59 | C22 | semidirect |
| 20. Dic944 | C22 | semidirect |
| 21. #16837242 | C22 | semidirect |
| 22. #16837241 | C22 | semidirect |
| 23. #16837240 | C22 | semidirect |
| 24. #16837239 | C22 | semidirect |
| 25. D1888 | C22 | semidirect |
| 26. #16837237 | C22 | semidirect |
| 27. #16837235 | C22 | semidirect |
| 28. #16837235 | C22 | semidirect |
| 29. C2×C59⋊C32 | C22 | semidirect |
| 30. C59×#508 | C22 | semidirect |
| 31. C59×Q64 | C22 | semidirect |
| 32. C59×SD64 | C22 | semidirect |
| 33. C59×D32 | C22 | semidirect |
| 34. C2×C32×C59 | C22 | semidirect |
| 134. #2262 | D59 | semidirect |
| 147. #508 | C2×D59 | semidirect |
| 154. Q64 | C2×D59 | semidirect |
| 158. SD64 | C2×D59 | semidirect |
| 161. D32 | C2×D59 | semidirect |
| 165. C2×C32 | C2×D59 | semidirect |
| 166. C59 | #33981 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #508×D59 | 2 |
| #21426415 | 2 |
| #21426412 | 2 |
| #21426410 | 2 |
| #21426407 | 2 |
| #21426405 | 2 |
| #21426403 | 2 |
| C2×#16837235 | 2 |
| C59×#2262 | 2 |
| #33981 | 59 |