Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
3550 conjugacy classes of subgroups; only the 627 normal subgroups are shown.
This group has 3550 conjugacy classes of subgroups — too many to draw. Only its 627 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. #21432348 | C2 | direct (N × H) |
| 2. C2×#16837315 | C2 | semidirect |
| 3. C2×#16837314 | C2 | semidirect |
| 4. C2×#16837313 | C2 | semidirect |
| 6. C2×C59×#393 | C2 | semidirect |
| 8. C23×Dic118 | C22 | semidirect |
| 12. #16837315 | C22 | semidirect |
| 13. #16837314 | C22 | semidirect |
| 14. #16837313 | C22 | semidirect |
| 16. C2×C59⋊#95 | C22 | semidirect |
| 17. C2×C59⋊#95 | C22 | semidirect |
| 18. C23×Q8×C59 | C22 | semidirect |
| 20. C59×#393 | C22 | semidirect |
| 21. C2×#95×C59 | C22 | semidirect |
| 24. C24×D59 | Q8 | semidirect |
| 29. C22×Dic118 | C23 | semidirect |
| 37. C59⋊#95 | C23 | semidirect |
| 38. C59⋊#95 | C23 | semidirect |
| 41. C22×Q8×C59 | C23 | semidirect |
| 46. #95×C59 | C23 | semidirect |
| 60. C23×D59 | C2×Q8 | semidirect |
| 136. C2×#393 | D59 | semidirect |
| 139. C2×C59 | #2840 | semidirect |
| 146. C23×Q8 | C2×D59 | semidirect |
| 154. #393 | C2×D59 | semidirect |
| 158. C2×#95 | C2×D59 | semidirect |
| 159. C59 | C2×#2840 | semidirect |
| 170. C22×Q8 | C22×D59 | semidirect |
| 184. #95 | C22×D59 | semidirect |
| 271. C2 | #21432348 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21432348 | 2 |
| C2×#16837315 | 2 |
| C2×#16837314 | 2 |
| C2×#16837313 | 2 |
| C2×#16837257 | 2 |
| C2×C59×#393 | 2 |
| C2×#2840 | 59 |