Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
982 conjugacy classes of subgroups; only the 199 normal subgroups are shown.
This group has 982 conjugacy classes of subgroups — too many to draw. Only its 199 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. #494×D59 | C2 | semidirect |
| 3. #486×D59 | C2 | semidirect |
| 4. #21423703 | C2 | semidirect |
| 5. #21423702 | C2 | semidirect |
| 6. #21423701 | C2 | semidirect |
| 7. #21423700 | C2 | semidirect |
| 8. C82×D59 | C2 | semidirect |
| 9. C59×#1709 | C2 | semidirect |
| 14. #16837782 | C22 | semidirect |
| 15. #16837781 | C22 | semidirect |
| 20. #16837750 | C22 | semidirect |
| 21. #16837749 | C22 | semidirect |
| 22. #16837748 | C22 | semidirect |
| 27. C8×C59⋊C8 | C22 | semidirect |
| 28. C8×C59⋊C8 | C22 | semidirect |
| 29. C59×#494 | C22 | semidirect |
| 31. C59×#486 | C22 | semidirect |
| 32. C82×C59 | C22 | semidirect |
| 149. #1709 | D59 | direct (N × H) |
| 155. D59 | #1709 | direct (N × H) |
| 163. #494 | C2×D59 | semidirect |
| 172. #486 | C2×D59 | semidirect |
| 178. C82 | C2×D59 | semidirect |
| 179. C59 | C2×#1709 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #494×D59 | 2 |
| #493×D59 | 2 |
| #486×D59 | 2 |
| #21423703 | 2 |
| #21423702 | 2 |
| #21423701 | 2 |
| #21423700 | 2 |
| C82×D59 | 2 |
| C59×#1709 | 2 |
| C2×#1709 | 59 |