Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
712 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 712 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. #21425613 | C2 | semidirect |
| 2. #21425611 | C2 | semidirect |
| 3. #21425495 | C2 | semidirect |
| 4. #21425494 | C2 | semidirect |
| 5. #21425493 | C2 | semidirect |
| 7. C59×#2069 | C2 | semidirect |
| 9. #16837451 | C22 | semidirect |
| 10. #16837450 | C22 | semidirect |
| 11. #16837450 | C22 | semidirect |
| 17. C59⋊#338 | C22 | semidirect |
| 18. C59×#430 | C22 | semidirect |
| 20. C59×#338 | C22 | semidirect |
| 113. #2069 | D59 | semidirect |
| 124. #430 | C2×D59 | semidirect |
| 132. #338 | C2×D59 | semidirect |
| 133. C59 | #32875 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21425613 | 2 |
| #21425611 | 2 |
| #21425495 | 2 |
| #21425494 | 2 |
| #21425493 | 2 |
| #21424015 | 2 |
| C59×#2069 | 2 |
| #32875 | 59 |